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Absolute Deviation (absolute + deviation)
Kinds of Absolute Deviation Selected AbstractsA mathematical programming approach for improving the robustness of least sum of absolute deviations regressionNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 4 2006Avi Giloni Abstract This paper discusses a novel application of mathematical programming techniques to a regression problem. While least squares regression techniques have been used for a long time, it is known that their robustness properties are not desirable. Specifically, the estimators are known to be too sensitive to data contamination. In this paper we examine regressions based on Least-sum of Absolute Deviations (LAD) and show that the robustness of the estimator can be improved significantly through a judicious choice of weights. The problem of finding optimum weights is formulated as a nonlinear mixed integer program, which is too difficult to solve exactly in general. We demonstrate that our problem is equivalent to a mathematical program with a single functional constraint resembling the knapsack problem and then solve it for a special case. We then generalize this solution to general regression designs. Furthermore, we provide an efficient algorithm to solve the general nonlinear, mixed integer programming problem when the number of predictors is small. We show the efficacy of the weighted LAD estimator using numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006 [source] Brain natriuretic peptide in the prediction of recurrence of angina pectorisEUROPEAN JOURNAL OF CLINICAL INVESTIGATION, Issue 2 2004H. Takase Abstract Background, Circulating levels of brain natriuretic peptide (BNP) provide prognostic information for patients with heart failure, but little is known about its prognostic usefulness in patients with stable angina pectoris. We investigated whether BNP could be used as a marker for the prediction of anginal recurrence after successful treatment. Design, Brain natriuretic peptide levels of 77 patients with stable angina pectoris were measured at enrolment and after confirmation of successful treatment (i.e. no anginal attack for at least 6 months: chronic phase) with percutaneous transluminal coronary angioplasty and/or conventional medication. Then, we prospectively followed them up for 25·9 ± 1·4 months, with the endpoint being a recurrence of anginal attacks. Results, An anginal attack recurred in seven patients. In patients without recurrence, BNP levels in the chronic phase (21 ± 12 [median ± median absolute deviation] pg mL,1) were lower than those measured at enrolment (46 ± 25 pg mL,1, P < 0·0001), whereas the levels in patients with recurrence increased during the same period (from 36 ± 16 to 72 ± 42 pg mL,1, P < 0·05). A univariate analysis revealed that the BNP level measured in the chronic phase was the significant predictor of future anginal recurrence. Analysis of the receiver operating characteristic curve indicated that the cutoff level of BNP in the chronic phase was 68 pg mL,1. The Kaplan-Meier method revealed that the incidence of anginal recurrence was higher in patients with higher (71·4%) than lower levels of BNP (2·9%; P < 0·0001). Conclusions, Measurement of BNP levels after successful therapy is clinically useful for the prediction of recurrence of anginal attacks in patients with angina pectoris. [source] Covert attention allows for continuous control of brain,computer interfacesEUROPEAN JOURNAL OF NEUROSCIENCE, Issue 8 2010Ali Bahramisharif Abstract While brain-computer interfaces (BCIs) can be used for controlling external devices, they also hold the promise of providing a new tool for studying the working brain. In this study we investigated whether modulations of brain activity by changes in covert attention can be used as a continuous control signal for BCI. Covert attention is the act of mentally focusing on a peripheral sensory stimulus without changing gaze direction. The ongoing brain activity was recorded using magnetoencephalography in subjects as they covertly attended to a moving cue while maintaining fixation. Based on posterior alpha power alone, the direction to which subjects were attending could be recovered using circular regression. Results show that the angle of attention could be predicted with a mean absolute deviation of 51° in our best subject. Averaged over subjects, the mean deviation was ,70°. In terms of information transfer rate, the optimal data length used for recovering the direction of attention was found to be 1700 ms; this resulted in a mean absolute deviation of 60° for the best subject. The results were obtained without any subject-specific feature selection and did not require prior subject training. Our findings demonstrate that modulations of posterior alpha activity due to the direction of covert attention has potential as a control signal for continuous control in a BCI setting. Our approach will have several applications, including a brain-controlled computer mouse and improved methods for neuro-feedback that allow direct training of subjects' ability to modulate posterior alpha activity. [source] Evaluation of DRAINMOD-S for simulating water table management under semi-arid conditions,IRRIGATION AND DRAINAGE, Issue 3 2002M. A. S. Wahba modèl e dela direction dela table d'eau souterraine; le drainage conventionnel; le drainage contrôlé Abstract The water table management simulation model, DRAINMOD-S, was evaluated under semi-arid conditions using field data from the Maruit experimental field in the western delta of Egypt for three cropping seasons; maize 1999, wheat 1999/2000 and maize 2000. Two water table management systems (conventional drainage (FD) and controlled drainage (CD)) were applied in the study area. The recorded data included daily ground water table depths, drain outflows during flow events, soil salinity to depth of 1.20 m from the soil surface (0.30 m interval), and relative crop yield. DRAINMOD-S was run to simulate the applied water table management systems for the same study periods. The reliability of the model was evaluated by comparing measured and predicted values of the daily ground water table depth, cumulative outflow based on total monthly outflow, soil salinity during each season, and relative crop yield. Good agreement was found between the measured and predicted values. DRAINMOD-S predicted values within an absolute deviation ranged from 11.0 to 16.0 cm for ground water table depth, from 18 to 75 mm for drain outflows, from 0.22 to 1.08 dS m,1 for soil salinity, and from 4.62 to 4.86% for relative crop yield. The model showed the potential for long-term simulation and planning of ground water table management systems under semi-arid conditions of the western delta of Egypt. Copyright © 2002 John Wiley & Sons, Ltd. RÉSUMÉ Le modèle DRAINMOD-S pour simuler la direction de la table d'eau sous des conditions demi-arides á été évalué en utilisant le data des champs experimentaux du Mariut delta denileouest d'Égypte pendant trois saisons agricoles: le maïs 1999, le blé 1999/2000 et le maïs 2000. Deux systèmes de direction de la table d'eau (drainage conventionnel (FD) et drainage contrôlé (CD)) ontété appliqués àla superficie de l'étude. Le data qui s'est remis en ordre s'inclut les mesures des profondeurs de la table d'eau souterraine, les écoulements des drains pendant les évènements de l'écoulement, la salinité du sol au profondeur de 1.20 m souterrain aux intervalles de 30 cm, etles produits agricoles relatifs. DRAINMOD-S S'est mis en courant pour simuler l'application des systèmes de la direction pour la même période d'étude. La véracité du modèle aété évaluée en comparant les valeurs mésurées avec lcelles des produits agricoles sur le profondeur de la table d'eau quotidien, l'écoulement cumulatif basé sur l'écoulement total du mois, la salinité du sol pendant chaque saison, et les produits agricoles relatifs. On a trouvé un bon accord entre les valeurs mésurées et celles qu'on avait prédites avec une déviation absolue qui rangeait de 11.0 à 16.0 cm pour la profondeur de la table d'eau, de 18 à 75 mm pour l'écoulement du drains, et de 0.22 à 1.08 dS m,1, pour la salinité du sol et de 4.62 à 4.86% pour les produits agricoles relatifs. Le modèle a indiqué une éfficacité pour une simulation allongée et pour projeter les systèmes de la direction dela table d'eau souterraine auprès les conditions demi-arides du delta ouest en Egypte. Copyright © 2002 John Wiley & Sons, Ltd. [source] Determination of rank by median absolute deviation (DRMAD): a simple method for determining the number of principal factors responsible for a data matrix,JOURNAL OF CHEMOMETRICS, Issue 1 2009Edmund R. Malinowski Abstract Median absolute deviation (MAD) is a well-established statistical method for determining outliers. This simple statistic can be used to determine the number of principal factors responsible for a data matrix by direct application to the residual standard deviation (RSD) obtained from principal component analysis (PCA). Unlike many other popular methods the proposed method, called determination of rank by MAD (DRMAD), does not involve the use of pseudo degrees of freedom, pseudo F -tests, extensive calibration tables, time-consuming iterations, nor empirical procedures. The method does not require strict adherence to normal distributions of experimental uncertainties. The computations are direct, simple to use and extremely fast, ideally suitable for online data processing. The results obtained using various sets of chemical data previously reported in the chemical literature agree with the early work. Limitations of the method, determined from model data, are discussed. An algorithm, written in MATLAB format, is presented in the Appendix. Copyright © 2008 John Wiley & Sons, Ltd. [source] Proton affinities of maingroup-element hydrides and noble gases: Trends across the periodic table, structural effects, and DFT validationJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 13 2006Marcel Swart Abstract We have carried out an extensive exploration of the gas-phase basicity of archetypal neutral bases across the periodic system using the generalized gradient approximation (GGA) of the density functional theory (DFT) at BP86/QZ4P//BP86/TZ2P. First, we validate DFT as a reliable tool for computing proton affinities and related thermochemical quantities: BP86/QZ4P//BP86/TZ2P is shown to yield a mean absolute deviation of 2.0 kcal/mol for the proton affinity at 298 K with respect to experiment, and 1.2 kcal/mol with high-level ab initio benchmark data. The main purpose of this work is to provide the proton affinities (and corresponding entropies) at 298 K of the neutral bases constituted by all maingroup-element hydrides of groups 15,17 and the noble gases, that is, group 18, and periods 1,6. We have also studied the effect of step-wise methylation of the protophilic center of the second- and third-period bases. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 1486,1493, 2006 [source] Transferable intermolecular potentials for carboxylic acids and their phase behaviorAICHE JOURNAL, Issue 2 2010Amir Vahid Abstract Transferable step potentials are characterized for 39 carboxylic acids. The reference potential is treated with discontinuous molecular dynamics, including detailed molecular structure. Thermodynamic perturbation theory is used to interpret the simulation results and to provide an efficient basis for molecular modeling and characterization of the attractive forces. Four steps are used for representation of the attractive forces with only the first and last steps varied independently. The two middle steps are interpolated such that each site type is characterized by three parameters: the diameter, ,, the depth of the inner well, ,1, and the depth of the outer well, ,4. The depths of the attractive wells are optimized to fit experimental vapor pressure and liquid density data. Generally, the vapor pressure is correlated to an overall 43% average absolute deviation (% AAD) and the liquid density to 5% AAD. The deviations tend to be largest for the higher molecular weight acids. These deviations are larger than the errors previously encountered in characterizing organic compounds, but carboxylic acids present exceptional challenges owing to their peculiar dimerization behavior. Simultaneous correlation of vapor pressure, vapor compressibility factor, and phase equilibria of water + carboxylic acids place several constraints on the nature of the potential model, with the parameters of the present model representing a reasonable tradeoff. In other words, our model represents minimal deviations for vapor pressure, vapor compressibility factor, and phase equilibria of all acids simultaneously while varying the parameters ,, ,1, ,4, ,CC(dimerizing site bonding energy), ,AD(acceptor-donor bonding energy), and KHB(hydrogen bonding volume) for the acid O and OH site types. The present model is characterized by one acceptor and one dimerizing site on the carbonyl oxygen and one acceptor and one donor site on the hydroxyl oxygen. The acceptor and donor are capable of interacting with water while the dimerizing site is not. With this model, the saturated vapor compressibility factor of acids with seven or fewer carbons is near 0.5 while higher carbon ratios lead to a compressibility factor approaching 1.0. To compensate for the high vapor pressure deviations of the transferable potential model, a correction is introduced to customize the molecule-molecule self interaction energy. This adaptation results in deviations of 3.1% for vapor pressure of the pure acid database. To validate the behavior of the model for carboxylic acids in mixtures, 33 binary solutions were considered. Acids in this database ranged from formic to hexadecanoic. The average absolute deviation in bubble pressure for aqueous acid systems is 4.4%, 10.5% for acid + acid systems, and 4.7% for acid + n-alkane systems without a customized interaction correction. When applying the correction, deviations were 2.4% for aqueous systems, 2% for acid systems, and 2.8% for acid + n-alkane systems. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] Sure independence screening for ultrahigh dimensional feature spaceJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 5 2008Jianqing Fan Summary., Variable selection plays an important role in high dimensional statistical modelling which nowadays appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality p, accuracy of estimation and computational cost are two top concerns. Recently, Candes and Tao have proposed the Dantzig selector using L1 -regularization and showed that it achieves the ideal risk up to a logarithmic factor log (p). Their innovative procedure and remarkable result are challenged when the dimensionality is ultrahigh as the factor log (p) can be large and their uniform uncertainty principle can fail. Motivated by these concerns, we introduce the concept of sure screening and propose a sure screening method that is based on correlation learning, called sure independence screening, to reduce dimensionality from high to a moderate scale that is below the sample size. In a fairly general asymptotic framework, correlation learning is shown to have the sure screening property for even exponentially growing dimensionality. As a methodological extension, iterative sure independence screening is also proposed to enhance its finite sample performance. With dimension reduced accurately from high to below sample size, variable selection can be improved on both speed and accuracy, and can then be accomplished by a well-developed method such as smoothly clipped absolute deviation, the Dantzig selector, lasso or adaptive lasso. The connections between these penalized least squares methods are also elucidated. [source] Fully Autonomous Preload-Sensitive Control of Implantable Rotary Blood PumpsARTIFICIAL ORGANS, Issue 9 2010Andreas Arndt Abstract A pulsatility-based control algorithm with a self-adapting pulsatility reference value is proposed for an implantable rotary blood pump and is to be tested in computer simulations. The only input signal is the pressure difference across the pump, which is deduced from measurements of the pump's magnetic bearing. A pulsatility index (PI) is calculated as the mean absolute deviation from the mean pressure difference. As a second characteristic, the gradient of the PI with respect to the pump speed is derived. This pulsatility gradient (GPI) is used as the controlled variable to adjust the operating point of the pump when physiological variables such as the systemic arterial pressure, left ventricular contractility, or heart rate change. Depending on the selected mode of operation, the controller is either a linear controller or an extremum-seeking controller. A supervisory mechanism monitors the state of the system and projects the system into the region of convergence when necessary. The controller of the GPI continuously adjusts the reference value for PI. An underlying robust linear controller regulates the PI to the reference value in order to take into account changes in pulmonary venous return. As a means of reacting to sudden changes in the venous return, a suction detection mechanism was included. The control system is robustly stable within a wide range of physiological variables. All the clinician needs to do is to select between the two operating modes. No other adjustments are required. The algorithm showed promising results which encourage further testing in vitro and in vivo. [source] High-Dimensional Cox Models: The Choice of Penalty as Part of the Model Building ProcessBIOMETRICAL JOURNAL, Issue 1 2010Axel Benner Abstract The Cox proportional hazards regression model is the most popular approach to model covariate information for survival times. In this context, the development of high-dimensional models where the number of covariates is much larger than the number of observations ( ) is an ongoing challenge. A practicable approach is to use ridge penalized Cox regression in such situations. Beside focussing on finding the best prediction rule, one is often interested in determining a subset of covariates that are the most important ones for prognosis. This could be a gene set in the biostatistical analysis of microarray data. Covariate selection can then, for example, be done by L1 -penalized Cox regression using the lasso (Tibshirani (1997). Statistics in Medicine16, 385,395). Several approaches beyond the lasso, that incorporate covariate selection, have been developed in recent years. This includes modifications of the lasso as well as nonconvex variants such as smoothly clipped absolute deviation (SCAD) (Fan and Li (2001). Journal of the American Statistical Association96, 1348,1360; Fan and Li (2002). The Annals of Statistics30, 74,99). The purpose of this article is to implement them practically into the model building process when analyzing high-dimensional data with the Cox proportional hazards model. To evaluate penalized regression models beyond the lasso, we included SCAD variants and the adaptive lasso (Zou (2006). Journal of the American Statistical Association101, 1418,1429). We compare them with "standard" applications such as ridge regression, the lasso, and the elastic net. Predictive accuracy, features of variable selection, and estimation bias will be studied to assess the practical use of these methods. We observed that the performance of SCAD and adaptive lasso is highly dependent on nontrivial preselection procedures. A practical solution to this problem does not yet exist. Since there is high risk of missing relevant covariates when using SCAD or adaptive lasso applied after an inappropriate initial selection step, we recommend to stay with lasso or the elastic net in actual data applications. But with respect to the promising results for truly sparse models, we see some advantage of SCAD and adaptive lasso, if better preselection procedures would be available. This requires further methodological research. [source] Weighted Wilcoxon-Type Smoothly Clipped Absolute Deviation MethodBIOMETRICS, Issue 2 2009Lan Wang Summary Shrinkage-type variable selection procedures have recently seen increasing applications in biomedical research. However, their performance can be adversely influenced by outliers in either the response or the covariate space. This article proposes a weighted Wilcoxon-type smoothly clipped absolute deviation (WW-SCAD) method, which deals with robust variable selection and robust estimation simultaneously. The new procedure can be conveniently implemented with the statistical software R. We establish that the WW-SCAD correctly identifies the set of zero coefficients with probability approaching one and estimates the nonzero coefficients with the rate n,1/2. Moreover, with appropriately chosen weights the WW-SCAD is robust with respect to outliers in both the x and y directions. The important special case with constant weights yields an oracle-type estimator with high efficiency in the presence of heavier-tailed random errors. The robustness of the WW-SCAD is partly justified by its asymptotic performance under local shrinking contamination. We propose a Bayesian information criterion type tuning parameter selector for the WW-SCAD. The performance of the WW-SCAD is demonstrated via simulations and by an application to a study that investigates the effects of personal characteristics and dietary factors on plasma beta-carotene level. [source] Acoustical Properties of Binary Mixtures of Heptane with Ethyl Acetate or Butyl AcetateCHINESE JOURNAL OF CHEMISTRY, Issue 3 2010Divya Shukla Abstract Mixed solvents rather than single pure liquids are of utmost practical importance in chemical and industrial processes as they provide an ample opportunity for the continuous adjustment of desired properties of the medium. Therefore, ultrasonic velocity (u) and density (,) were measured for the binary mixtures formed by heptane with ethyl acetate or butyl acetate at temperatures 293, 298 and 303 K over the entire composition range. Deviation in ultrasonic velocity (,u), deviation in isentropic compressibility (,,s), and excess intermolecular free length (LEf) have been evaluated using the ultrasonic velocity data and the computed results were fitted to the Redlich-Kister polynomial equation. The values of ,u, ,,s and LEf were plotted against the molar fraction of heptane. The observed positive and negative values of excess parameters were discussed in terms of molecular interaction between the components of the mixtures. Experimental values of ultrasonic velocity and density were compared with the results obtained by theoretical estimation procedures. The results were discussed in terms of average absolute deviation (AAD). [source] Threshold levels of purified natural Bos d 2 for inducing bronchial airway response in asthmatic patientsCLINICAL & EXPERIMENTAL ALLERGY, Issue 10 2002T. Zeiler Summary Background Provocation tests are invaluable in establishing threshold levels and a causal relationship between atopic asthma and a certain allergen source, especially in relation to work-associated exposure. Purified major allergens open possibilities for a more accurate assessment of sensitization. Objective To determine the threshold dose of purified major bovine dander allergen Bos d 2 in bronchial provocation in comparison with the standard allergen and a set of other parameters of allergy. Method Nine consecutive patients referred to hospital for confirming the bovine origin of their occupational asthma were subjected to bronchial provocation tests with purified natural Bos d 2 and a standard bovine dander allergen. Additional tests included bronchial histamine challenge, measurements of total IgE, specific IgE antibody determinations and skin prick tests (SPT) with both allergens. Results In the provocation tests with Bos d 2, a 15% decrease in the forced expiratory volume in 1 s (FEV1) and/or peak expiratory flow (PEF) values in eight out of nine patients confirmed the predominant role of Bos d 2 in the sensitization. The threshold dose of Bos d 2 varied from 0.1 µg to > 100 µg (median ± median absolute deviation = 4.5 ± 3.9 µg). A positive SPT was induced by a median dose of 13.9 ± 9.8 µg of Bos d 2. Bronchial response to histamine and IgE antibodies against Bos d 2 showed the highest correlations to the provocations results. Conclusions The efficacy of Bos d 2 in bronchial provocation in patients with occupational cattle-associated asthma was confirmed and the range of the threshold level was determined. There were individual variations, but the response in provocation remains the reference method for identification of the cause of occupational atopic asthma. SPT and the measurement of specific IgE antibodies, preferably with purified or recombinant major allergens, increase the accuracy of the diagnosis. [source] Energy landscapes of nucleophilic substitution reactions: A comparison of density functional theory and coupled cluster methodsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 9 2007Marcel Swart Abstract We have carried out a detailed evaluation of the performance of all classes of density functional theory (DFT) for describing the potential energy surface (PES) of a wide range of nucleophilic substitution (SN2) reactions involving, amongst others, nucleophilic attack at carbon, nitrogen, silicon, and sulfur. In particular, we investigate the ability of the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA as well as hybrid DFT to reproduce high-level coupled cluster (CCSD(T)) benchmarks that are close to the basis set limit. The most accurate GGA, meta-GGA, and hybrid functionals yield mean absolute deviations of about 2 kcal/mol relative to the coupled cluster data, for reactant complexation, central barriers, overall barriers as well as reaction energies. For the three nonlocal DFT classes, the best functionals are found to be OPBE (GGA), OLAP3 (meta-GGA), and mPBE0KCIS (hybrid DFT). The popular B3LYP functional is not bad but performs significantly worse than the best GGA functionals. Furthermore, we have compared the geometries from several density functionals with the reference CCSD(T) data. The same GGA functionals that perform best for the energies (OPBE, OLYP), also perform best for the geometries with average absolute deviations in bond lengths of 0.06 Å and 0.6°, even better than the best meta-GGA and hybrid functionals. In view of the reduced computational effort of GGAs with respect to meta-GGAs and hybrid functionals, let alone coupled cluster, we recommend the use of accurate GGAs such as OPBE or OLYP for the study of SN2 reactions. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007 [source] Converging free energy estimates: MM-PB(GB)SA studies on the protein,protein complex Ras,RafJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 2 2004Holger Gohlke Abstract Estimating protein,protein interaction energies is a very challenging task for current simulation protocols. Here, absolute binding free energies are reported for the complex H-Ras/C-Raf1 using the MM-PB(GB)SA approach, testing the internal consistency and model dependence of the results. Averaging gas-phase energies (MM), solvation free energies as determined by Generalized Born models (GB/SA), and entropic contributions calculated by normal mode analysis for snapshots obtained from 10 ns explicit-solvent molecular dynamics in general results in an overestimation of the binding affinity when a solvent-accessible surface area-dependent model is used to estimate the nonpolar solvation contribution. Applying the sum of a cavity solvation free energy and explicitly modeled solute,solvent van der Waals interaction energies instead provides less negative estimates for the nonpolar solvation contribution. When the polar contribution to the solvation free energy is determined by solving the Poisson,Boltzmann equation (PB) instead, the calculated binding affinity strongly depends on the atomic radii set chosen. For three GB models investigated, different absolute deviations from PB energies were found for the unbound proteins and the complex. As an alternative to normal-mode calculations, quasiharmonic analyses have been performed to estimate entropic contributions due to changes of solute flexibility upon binding. However, such entropy estimates do not converge after 10 ns of simulation time, indicating that sampling issues may limit the applicability of this approach. Finally, binding free energies estimated from snapshots of the unbound proteins extracted from the complex trajectory result in an underestimate of binding affinity. This points to the need to exercise caution in applying the computationally cheaper "one-trajectory-alternative" to systems where there may be significant changes in flexibility and structure due to binding. The best estimate for the binding free energy of Ras,Raf obtained in this study of ,8.3 kcal mol,1 is in good agreement with the experimental result of ,9.6 kcal mol,1, however, further probing the transferability of the applied protocol that led to this result is necessary. © 2003 Wiley Periodicals, Inc. J Comput Chem 2: 238,250, 2003 [source] Prediction and nonparametric estimation for time series with heavy tailsJOURNAL OF TIME SERIES ANALYSIS, Issue 3 2002PETER HALL Motivated by prediction problems for time series with heavy-tailed marginal distributions, we consider methods based on `local least absolute deviations' for estimating a regression median from dependent data. Unlike more conventional `local median' methods, which are in effect based on locally fitting a polynomial of degree 0, techniques founded on local least absolute deviations have quadratic bias right up to the boundary of the design interval. Also in contrast to local least-squares methods based on linear fits, the order of magnitude of variance does not depend on tail-weight of the error distribution. To make these points clear, we develop theory describing local applications to time series of both least-squares and least-absolute-deviations methods, showing for example that, in the case of heavy-tailed data, the conventional local-linear least-squares estimator suffers from an additional bias term as well as increased variance. [source] Theoretical investigation on multinuclear NMR chemical shifts of some tris(trifluoromethyl)boron complexesMAGNETIC RESONANCE IN CHEMISTRY, Issue 8 2009Jun Zhang Abstract Tris(trifluoromethyl)boron complexes have unusual properties and may find applications in many fields of chemistry, biology, and physics. To gain insight into their NMR properties, the isotropic 11B, 13C, and 19F NMR chemical shifts of a series of tris(trifluoromethyl)boron complexes were systematically studied using the gauge-included atomic orbitals (GIAO) method at the levels of B3LYP/6-31 + G(d,p)//B3LYP/6-31G* and B3LYP/6-311 + G(d,p)//B3LYP/6-311 + G(d,p). Solvent effects were taken into account by polarizable continuum models (PCM). The calculated results were compared with the experimental values. The reason that the structurally inequivalent fluorine atoms in a specific species give a same chemical shift in experimental measurements is attributed to the fast rotation of CF3 group around the BC(F3) bond because of the low energy barrier. The calculated 11B, 13C(F3), and 19F chemical shifts are in good agreement with the experimental measurements, while the deviations of calculated 13C(X, X = O, N) chemical shifts are slightly large. For the latter, the average absolute deviations of the results from B3LYP/6-311 + G(d,p)//B3LYP/6-311 + G(d,p) are smaller than those from B3LYP/6-31 + G(d,p)//B3LYP/6-31G*, and the inclusion of PCM reduces the deviation values. The calculated 19F and 11B chemical shieldings of (CF3)3BCO are greatly dependent on the optimized structures, while the influence of structural parameters on the calculated 13C chemical shieldings is minor. Copyright © 2009 John Wiley & Sons, Ltd. [source] Two Typical Examples of Scaling Ionic Partition Scheme for Estimating Correlation Energy of A2 Type MoleculesCHINESE JOURNAL OF CHEMISTRY, Issue 4 2004Shu-Ping Zhuo Abstract Based on the calculation results of pair correlation energy contributions of the various electron pairs in Naz and H2NNH2 systems and the application of the scaling ionic partition scheme for symmetrical A2 type systems, the total correlation energies of Na2 and H2NNH2 have been reproduced by using this simple scheme. The two results show that the absolute deviations are within an acceptable range of mr, however, in this way, more than 90% of computational work can be. saved. The most attractive result in present paper is that, in these two molecules the coefficients c1 and c2 in the estimation equation can be obtained by the proportion of correlation energy of A, to that of A+ singlet system. Therefore, it is believed that the proposed ionic partition scheme for symmetrical A2 molecules would be very useful to estimate the correlation energies of large symmetrical molecules. [source] Prediction and nonparametric estimation for time series with heavy tailsJOURNAL OF TIME SERIES ANALYSIS, Issue 3 2002PETER HALL Motivated by prediction problems for time series with heavy-tailed marginal distributions, we consider methods based on `local least absolute deviations' for estimating a regression median from dependent data. Unlike more conventional `local median' methods, which are in effect based on locally fitting a polynomial of degree 0, techniques founded on local least absolute deviations have quadratic bias right up to the boundary of the design interval. Also in contrast to local least-squares methods based on linear fits, the order of magnitude of variance does not depend on tail-weight of the error distribution. To make these points clear, we develop theory describing local applications to time series of both least-squares and least-absolute-deviations methods, showing for example that, in the case of heavy-tailed data, the conventional local-linear least-squares estimator suffers from an additional bias term as well as increased variance. [source] | |||||||||||||||||||