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Selected AbstractsA Three-step Method for Choosing the Number of Bootstrap RepetitionsECONOMETRICA, Issue 1 2000Donald W. K. Andrews This paper considers the problem of choosing the number of bootstrap repetitions B for bootstrap standard errors, confidence intervals, confidence regions, hypothesis tests, p -values, and bias correction. For each of these problems, the paper provides a three-step method for choosing B to achieve a desired level of accuracy. Accuracy is measured by the percentage deviation of the bootstrap standard error estimate, confidence interval length, test's critical value, test's p -value, or bias-corrected estimate based on B bootstrap simulations from the corresponding ideal bootstrap quantities for which B=,. The results apply quite generally to parametric, semiparametric, and nonparametric models with independent and dependent data. The results apply to the standard nonparametric iid bootstrap, moving block bootstraps for time series data, parametric and semiparametric bootstraps, and bootstraps for regression models based on bootstrapping residuals. Monte Carlo simulations show that the proposed methods work very well. [source] Matched interface and boundary (MIB) method for the vibration analysis of platesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2009S. N. Yu Abstract This paper proposes a novel approach, the matched interface and boundary (MIB) method, for the vibration analysis of rectangular plates with simply supported, clamped and free edges, and their arbitrary combinations. In previous work, the MIB method was developed for three-dimensional elliptic equations with arbitrarily complex material interfaces and geometric shapes. The present work generalizes the MIB method for eigenvalue problems in structural analysis with complex boundary conditions. The MIB method utilizes both uniform and non-uniform Cartesian grids. Fictitious values are utilized to facilitate the central finite difference schemes throughout the entire computational domain. Boundary conditions are enforced with fictitious values,a common practice used in the previous discrete singular convolution algorithm. An essential idea of the MIB method is to repeatedly use the boundary conditions to achieve arbitrarily high-order accuracy. A new feature in the proposed approach is the implementation of the cross derivatives in the free boundary conditions. The proposed method has a banded matrix. Nine different plates, particularly those with free edges and free corners, are employed to validate the proposed method. The performance of the proposed method is compared with that of other established methods. Convergence and comparison studies indicate that the proposed MIB method works very well for the vibration analysis of plates. In particular, modal bending moments and shear forces predicted by the proposed method vanish at boundaries for free edges. Copyright © 2008 John Wiley & Sons, Ltd. [source] The S and G transformations for computing three-center nuclear attraction integralsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 8 2009Richard Mikael Slevinsky Abstract It is now well established that nonlinear transformations can be extremely useful in the case of oscillatory integrals. In previous work, we could show that the G transformation, which is not so well known among those interested in the numerical evaluation of highly oscillatory integrals, works very well for the extremely challenging integral called Twisted Tail. In this work, we demonstrate that these techniques also apply to three-center nuclear attraction integrals over exponential type functions. The accurate and rapid evaluation of these integrals is required in ab initio molecular structure calculations and density functional theory. Using a basis set of B functions and profiting from their relatively simple Fourier representation, these integrals are formulated as analytical expressions involving highly oscillatory spherical Bessel integral functions. In the present work, we implement two highly accurate algorithms for three-center nuclear attraction integrals. The first algorithm is based on the G transformation and the second is based on a combination of the S and G transformations. The application of these transformations is largely due to the properties of special functions that allow the computation of higher order derivatives of the integrands with exceptional simplicity. The numerical results illustrate the accuracy of these algorithms applied to three-center nuclear attraction integrals over exponential type functions with a miscellany of different parameters. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] A deconvolution method for the reconstruction of underlying profiles measured using large sampling volumesJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 3 2006Y.-S. Xiong A deconvolution method for diffraction measurements based on a statistical learning technique is presented. The radial-basis function network is used to model the underlying function. A full probabilistic description of the measurement is introduced, incorporating a Bayesian algorithm based on an evidence framework. This method allows predictions of both the convolution and the underlying function from noisy measurements. In addition, the method can provide an estimation of the prediction uncertainty, i.e. error-bars. In order to assess the capability of the method, the model was tested first on synthetic data of controllable quality and sparsity; it is shown that the method works very well, even for inaccurately measured (noisy) data. Subsequently, the deconvolution method was applied to real data sets typical of neutron and synchrotron residual stress (strain) data, recovering features not immediately evident in the large-gauge-volume measurements themselves. Finally, the extent to which short-period components are lost as a function of the measurement gauge dimensions is discussed. The results seem to indicate that for a triangular sensor-sensitivity function, measurements are best made with a gauge of a width approximately equal to the wavelength of the expected strain variation, but with a significant level of overlap (,80%) between successive points; this is contrary to current practice for neutron strain measurements. [source] A forecasting procedure for nonlinear autoregressive time series modelsJOURNAL OF FORECASTING, Issue 5 2005Yuzhi CaiArticle first published online: 2 AUG 200 Abstract Forecasting for nonlinear time series is an important topic in time series analysis. Existing numerical algorithms for multi-step-ahead forecasting ignore accuracy checking, alternative Monte Carlo methods are also computationally very demanding and their accuracy is difficult to control too. In this paper a numerical forecasting procedure for nonlinear autoregressive time series models is proposed. The forecasting procedure can be used to obtain approximate m -step-ahead predictive probability density functions, predictive distribution functions, predictive mean and variance, etc. for a range of nonlinear autoregressive time series models. Examples in the paper show that the forecasting procedure works very well both in terms of the accuracy of the results and in the ability to deal with different nonlinear autoregressive time series models. Copyright © 2005 John Wiley & Sons, Ltd. [source] A Bayesian threshold nonlinearity test for financial time seriesJOURNAL OF FORECASTING, Issue 1 2005Mike K. P. So Abstract We propose in this paper a threshold nonlinearity test for financial time series. Our approach adopts reversible-jump Markov chain Monte Carlo methods to calculate the posterior probabilities of two competitive models, namely GARCH and threshold GARCH models. Posterior evidence favouring the threshold GARCH model indicates threshold nonlinearity or volatility asymmetry. Simulation experiments demonstrate that our method works very well in distinguishing GARCH and threshold GARCH models. Sensitivity analysis shows that our method is robust to misspecification in error distribution. In the application to 10 market indexes, clear evidence of threshold nonlinearity is discovered and thus supporting volatility asymmetry. Copyright © 2005 John Wiley & Sons, Ltd. [source] A Bayesian nonlinearity test for threshold moving average modelsJOURNAL OF TIME SERIES ANALYSIS, Issue 5 2010Qiang Xia We propose a Bayesian test for nonlinearity of threshold moving average (TMA) models. First, we obtain the marginal posterior densities of all parameters, including the threshold and delay, of the TMA model using Gibbs sampler with the Metropolis,Hastings algorithm. And then, we adopt reversible-jump Markov chain Monte Carlo methods to calculate the posterior probabilities for MA and TMA models. Posterior evidence in favour of the TMA model indicates threshold nonlinearity. Simulation experiments and a real example show that our method works very well in distinguishing MA and TMA models. [source] Towards the best model for H atoms in experimental charge-density refinementACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2009Anna A. Hoser The consequences of different treatments of H atoms in experimental charge-density studies are discussed. Geometric and topological parameters obtained after applying four different H-atom models in multipolar refinement on high-resolution X-ray data only were compared with the results obtained for a reference joint high-resolution X-ray/neutron refinement. The geometry and the topological critical point and integrated parameters closest to the reference values were obtained after a mixed refinement (high-order refinement of heavy atoms, low-angle refinement of H atoms and elongation of the X,H distance to the average neutron bond lengths) supplemented by an estimation of the anisotropic thermal motions of H atoms using the SHADE program. Such a procedure works very well even for strong hydrogen bonds. The worst fit to the reference results for both critical point and integrated parameters was obtained when only the standardization to the average neutron X,H distances was applied. The non-H-atom parameters are also systematically influenced by the H-atom modeling. In order to compare topological and integrated properties calculated for H and non-H atoms in multipolar refinement when there are no neutron data, the same treatment of H atoms (ideally the mixed refinement + estimated anisotropic atomic displacement parameters for H atoms) should be applied. [source] Ridge regression in two-parameter solutionAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 6 2005Stan Lipovetsky Abstract We consider simultaneous minimization of the model errors, deviations from orthogonality between regressors and errors, and deviations from other desired properties of the solution. This approach corresponds to a regularized objective that produces a consistent solution not prone to multicollinearity. We obtain a generalization of the ridge regression to two-parameter model that always outperforms a regular one-parameter ridge by better approximation, and has good properties of orthogonality between residuals and predicted values of the dependent variable. The results are very convenient for the analysis and interpretation of the regression. Numerical runs prove that this technique works very well. The examples are considered for marketing research problems. Copyright © 2005 John Wiley & Sons, Ltd. [source] | ||||||||||||||||