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Regression Functions (regression + function)

Distribution by Scientific Domains

Mathematics and Statistics	38%
Business, Economics, Finance and Accounting	38%

Selected Abstracts

Identification and Estimation of Regression Models with Misclassification

ECONOMETRICA, Issue 3 2006
Aprajit Mahajan
This paper studies the problem of identification and estimation in nonparametric regression models with a misclassified binary regressor where the measurement error may be correlated with the regressors. We show that the regression function is nonparametrically identified in the presence of an additional random variable that is correlated with the unobserved true underlying variable but unrelated to the measurement error. Identification for semiparametric and parametric regression functions follows straightforwardly from the basic identification result. We propose a kernel estimator based on the identification strategy, derive its large sample properties, and discuss alternative estimation procedures. We also propose a test for misclassification in the model based on an exclusion restriction that is straightforward to implement. [source]

Determination of cationic mobilities and pKa values of 22 amino acids by capillary zone electrophoresis

ELECTROPHORESIS, Issue 2 2004
eláková, ina V
Abstract The effective mobilities of the cationic forms of common amino acids , mostly proteinogenic , were determined by capillary zone electrophoresis in acidic background electrolytes at pH between 2.0 and 3.2. The underivatized amino acids were detected by the double contactless conductivity detector. Experimentally measured effective mobilities were fitted with the suitable regression functions in dependence on pH of the background electrolyte. The parameters of the given regression function corresponded to the values of the actual mobilities and the mixed dissociation constants (combining activities and concentrations) of the compound related to the actual ionic strength. McInnes approximation and Onsager theory were used to obtain thermodynamic dissociation constants (pKa) and limiting (absolute) ionic mobilities. [source]

Wavelet change-point estimation for long memory non-parametric random design models

JOURNAL OF TIME SERIES ANALYSIS, Issue 2 2010
Lihong Wang
62G08; 62G05; 62G20 For a random design regression model with long memory design and long memory errors, we consider the problem of detecting a change point for sharp cusp or jump discontinuity in the regression function. Using the wavelet methods, we obtain estimators for the change point, the jump size and the regression function. The strong consistencies of these estimators are given in terms of convergence rates. [source]

Nonlinear econometric models with cointegrated and deterministically trending regressors

THE ECONOMETRICS JOURNAL, Issue 1 2001
Yoosoon Chang
This paper develops an asymptotic theory for a general class of nonlinear non-stationary regressions, extending earlier work by Phillips and Hansen (1990) on linear cointegrating regressions. The model considered accommodates a linear time trend and stationary regressors, as well as multiple I(1) regressors. We establish consistency and derive the limit distribution of the nonlinear least squares estimator. The estimator is consistent under fairly general conditions but the convergence rate and the limiting distribution are critically dependent upon the type of the regression function. For integrable regression functions, the parameter estimates converge at a reduced n1/4 rate and have mixed normal limit distributions. On the other hand, if the regression functions are homogeneous at infinity, the convergence rates are determined by the degree of the asymptotic homogeneity and the limit distributions are non-Gaussian. It is shown that nonlinear least squares generally yields inefficient estimators and invalid tests, just as in linear nonstationary regressions. The paper proposes a methodology to overcome such difficulties. The approach is simple to implement, produces efficient estimates and leads to tests that are asymptotically chi-square. It is implemented in empirical applications in much the same way as the fully modified estimator of Phillips and Hansen. [source]

Effectiveness of neural networks to regression with structural changes

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2002
Miyoko Asano
Abstract This paper reports simple numerical experiments of the application of multi-layered and feed-forward neural networks to regression with change points to clarify one of the effectiveness of the neural network model compared with non-parametric regression methods based on scatter plot smoothing. We also show an illustrative example, which successfully draws too rapid growth of GDP in Japan at the bubble economy around 1990 by interpreting decomposition of regression function suggested by the optimal neural networks fitting. Copyright © 2002 John Wiley & Sons, Ltd. [source]

ACCELERATED FAILURE TIME MODELS WITH NONLINEAR COVARIATES EFFECTS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2007
Chenlei Leng
Summary As a flexible alternative to the Cox model, the accelerated failure time (AFT) model assumes that the event time of interest depends on the covariates through a regression function. The AFT model with non-parametric covariate effects is investigated, when variable selection is desired along with estimation. Formulated in the framework of the smoothing spline analysis of variance model, the proposed method based on the Stute estimate (Stute, 1993[Consistent estimation under random censorship when covariables are present, J. Multivariate Anal.45, 89,103]) can achieve a sparse representation of the functional decomposition, by utilizing a reproducing kernel Hilbert norm penalty. Computational algorithms and theoretical properties of the proposed method are investigated. The finite sample size performance of the proposed approach is assessed via simulation studies. The primary biliary cirrhosis data is analyzed for demonstration. [source]

PLUG-IN ESTIMATION OF GENERAL LEVEL SETS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 1 2006
Antonio Cuevas
Summary Given an unknown function (e.g. a probability density, a regression function, ,) f and a constant c, the problem of estimating the level set L(c) ={f,c} is considered. This problem is tackled in a very general framework, which allows f to be defined on a metric space different from . Such a degree of generality is motivated by practical considerations and, in fact, an example with astronomical data is analyzed where the domain of f is the unit sphere. A plug-in approach is followed; that is, L(c) is estimated by Ln(c) ={fn,c}, where fn is an estimator of f. Two results are obtained concerning consistency and convergence rates, with respect to the Hausdorff metric, of the boundaries ,Ln(c) towards ,L(c). Also, the consistency of Ln(c) to L(c) is shown, under mild conditions, with respect to the L1 distance. Special attention is paid to the particular case of spherical data. [source]

Cutpoint Selection for Categorizing a Continuous Predictor

BIOMETRICS, Issue 2 2004
Sean M. O'Brien
Summary. This article presents a new approach for choosing the number of categories and the location of category cutpoints when a continuous exposure variable needs to be categorized to obtain tabular summaries of the exposure effect. The optimum categorization is defined as the partition that minimizes a measure of distance between the true expected value of the outcome for each subject and the estimated average outcome among subjects in the same exposure category. To estimate the optimum partition, an efficient nonparametric estimate of the unknown regression function is substituted into a formula for the asymptotically optimum categorization. This new approach is easy to implement and it outperforms existing cutpoint selection methods. [source]

Semiparametric Regression Modeling with Mixtures of Berkson and Classical Error, with Application to Fallout from the Nevada Test Site

BIOMETRICS, Issue 1 2002
Bani Mallick
Summary. We construct Bayesian methods for semiparametric modeling of a monotonic regression function when the predictors are measured with classical error, Berkson error, or a mixture of the two. Such methods require a distribution for the unobserved (latent) predictor, a distribution we also model semi-parametrically. Such combinations of semiparametric methods for the dose-response as well as the latent variable distribution have not been considered in the measurement error literature for any form of measurement error. In addition, our methods represent a new approach to those problems where the measurement error combines Berkson and classical components. While the methods are general, we develop them around a specific application, namely, the study of thyroid disease in relation to radiation fallout from the Nevada test site. We use this data to illustrate our methods, which suggest a point estimate (posterior mean) of relative risk at high doses nearly double that of previous analyses but that also suggest much greater uncertainty in the relative risk. [source]

Decision Theory Applied to an Instrumental Variables Model

ECONOMETRICA, Issue 3 2007
Gary Chamberlain
This paper applies some general concepts in decision theory to a simple instrumental variables model. There are two endogenous variables linked by a single structural equation; k of the exogenous variables are excluded from this structural equation and provide the instrumental variables (IV). The reduced-form distribution of the endogenous variables conditional on the exogenous variables corresponds to independent draws from a bivariate normal distribution with linear regression functions and a known covariance matrix. A canonical form of the model has parameter vector (,, ,, ,), where ,is the parameter of interest and is normalized to be a point on the unit circle. The reduced-form coefficients on the instrumental variables are split into a scalar parameter ,and a parameter vector ,, which is normalized to be a point on the (k,1)-dimensional unit sphere; ,measures the strength of the association between the endogenous variables and the instrumental variables, and ,is a measure of direction. A prior distribution is introduced for the IV model. The parameters ,, ,, and ,are treated as independent random variables. The distribution for ,is uniform on the unit circle; the distribution for ,is uniform on the unit sphere with dimension k-1. These choices arise from the solution of a minimax problem. The prior for ,is left general. It turns out that given any positive value for ,, the Bayes estimator of ,does not depend on ,; it equals the maximum-likelihood estimator. This Bayes estimator has constant risk; because it minimizes average risk with respect to a proper prior, it is minimax. The same general concepts are applied to obtain confidence intervals. The prior distribution is used in two ways. The first way is to integrate out the nuisance parameter ,in the IV model. This gives an integrated likelihood function with two scalar parameters, ,and ,. Inverting a likelihood ratio test, based on the integrated likelihood function, provides a confidence interval for ,. This lacks finite sample optimality, but invariance arguments show that the risk function depends only on ,and not on ,or ,. The second approach to confidence sets aims for finite sample optimality by setting up a loss function that trades off coverage against the length of the interval. The automatic uniform priors are used for ,and ,, but a prior is also needed for the scalar ,, and no guidance is offered on this choice. The Bayes rule is a highest posterior density set. Invariance arguments show that the risk function depends only on ,and not on ,or ,. The optimality result combines average risk and maximum risk. The confidence set minimizes the average,with respect to the prior distribution for ,,of the maximum risk, where the maximization is with respect to ,and ,. [source]

Identification and Estimation of Regression Models with Misclassification

Identification in Nonseparable Models

ECONOMETRICA, Issue 5 2003
Andrew Chesher
Weak nonparametric restrictions are developed, sufficient to identify the values of derivatives of structural functions in which latent random variables are nonseparable. These derivatives can exhibit stochastic variation. In a microeconometric context this allows the impact of a policy intervention, as measured by the value of a structural derivative, to vary across people who are identical as measured by covariates. When the restrictions are satisfied quantiles of the distribution of a policy impact across people can be identified. The identification restrictions are local in the sense that they are specific to the values of the covariates and the specific quantiles of latent variables at which identification is sought. The conditions do not include the commonly required independence of latent variables and covariates. They include local versions of the classical rank and order conditions and local quantile insensitivity conditions. Values of structural derivatives are identified by functionals of quantile regression functions and can be estimated using the same functionals applied to estimated quantile regression functions. [source]

Determination of cationic mobilities and pKa values of 22 amino acids by capillary zone electrophoresis

Nonparametric harmonic regression for estuarine water quality data

ENVIRONMETRICS, Issue 6 2010
Melanie A. Autin
Abstract Periodicity is omnipresent in environmental time series data. For modeling estuarine water quality variables, harmonic regression analysis has long been the standard for dealing with periodicity. Generalized additive models (GAMs) allow more flexibility in the response function. They permit parametric, semiparametric, and nonparametric regression functions of the predictor variables. We compare harmonic regression, GAMs with cubic regression splines, and GAMs with cyclic regression splines in simulations and using water quality data collected from the National Estuarine Reasearch Reserve System (NERRS). While the classical harmonic regression model works well for clean, near-sinusoidal data, the GAMs are competitive and are very promising for more complex data. The generalized additive models are also more adaptive and require less-intervention. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Valuing avoided morbidity using meta-regression analysis: what can health status measures and QALYs tell us about WTP?

HEALTH ECONOMICS, Issue 8 2006
George Van Houtven
Abstract Many economists argue that willingness-to-pay (WTP) measures are most appropriate for assessing the welfare effects of health changes. Nevertheless, the health evaluation literature is still dominated by studies estimating nonmonetary health status measures (HSMs), which are often used to assess changes in quality-adjusted life years (QALYs). Using meta-regression analysis, this paper combines results from both WTP and HSM studies applied to acute morbidity, and it tests whether a systematic relationship exists between HSM and WTP estimates. We analyze over 230 WTP estimates from 17 different studies and find evidence that QALY-based estimates of illness severity , as measured by the Quality of Well-Being (QWB) Scale , are significant factors in explaining variation in WTP, as are changes in the duration of illness and the average income and age of the study populations. In addition, we test and reject the assumption of a constant WTP per QALY gain. We also demonstrate how the estimated meta-regression equations can serve as benefit transfer functions for policy analysis. By specifying the change in duration and severity of the acute illness and the characteristics of the affected population, we apply the regression functions to predict average WTP per case avoided. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Reasoning about non-linear AR models using expectation maximization

JOURNAL OF FORECASTING, Issue 6-7 2003
M. ArnoldArticle first published online: 19 SEP 200
Abstract A simplified version of the expectation maximization (EM) algorithm is applied to search for optimal state sequences in state-dependent AR models whereby no prior knowledge about the state equation is necessary. These sequences can be used to draw conclusions about functional dependencies between the observed process and estimated AR coefficients. Consequently this approach is especially helpful in the identification of functional,coefficient AR models where the coefficients are controlled by the process itself. The approximation of regression functions in first-order non-linear AR models and the localization of multiple thresholds in self-exciting threshold autoregressive models are demonstrated as examples.,Copyright © 2003 John Wiley & Sons, Ltd. [source]

Estimating water retention curves of forest soils from soil texture and bulk density

JOURNAL OF PLANT NUTRITION AND SOIL SCIENCE, Issue 1 2003
Robert Teepe
Abstract Forest soils differ significantly from the arable land in their distribution of the soil bulk density and humus content, but the water retention parameters are primarily derived from the data of agricultural soils. Thus, there is a need to relate physical parameters of forest soils with their water retention characteristics and compare them with those of agricultural soils. Using 1850 water retention curves from forest soils, we related the following soil physical parameters to soil texture, bulk density, and C content: air capacity (AC), available water capacity (AWC), and the permanent wilting point (PWP). The ACs of forest soils were significantly higher than those of agricultural soils which were related to the low bulk densities of the forest soils, whereas differences in AWCs were small. Therefore, for a proper evaluation of the water retention curves (WRCs) and the parameters derived from them, further subdivisions of the lowest (< 1.45 g cm -3) of the three bulk density classes was undertaken to the wide range of low soil densities in forest soils (giving a total of 5 bulk density classes). In Germany, 31 soil texture classes are used for the estimation of soil physical parameters. Such a detailed classification is not required because of insignificant differences in WRCs for a large number of these classes. Based on cluster analysis of AC, AWC, and PWP parameters, 10 texture collectives were obtained. Using 5 classes of bulk densities, we further calculated the ACs, AWCs, and the PWPs for these 10 classes. Furthermore, "van Genuchten parameters" (, r, , s, ,, and n) were derived which described the average WRC for each designated class. In a second approach using multiple regression analysis, regression functions for AC, AWC, and PWP and for the van Genuchten parameter were calculated. Abschätzung der Wasser-Retentionskurven von Waldböden anhand der Bodenart und Bodendichte Obwohl sich Waldböden in der Verteilung der Bodendichte und Humusgehalte deutlich von Ackerböden unterscheiden, basiert die Ableitung ihrer bodenphysikalischen Kenngrößen in der Kartieranleitung auf Erhebungen landwirtschaftlich genutzter Böden. Die Abschätzung physikalischer Eigenschaften von Waldböden ist daher weiterhin als unzureichend anzusehen. In dieser Arbeit wurde auf Grundlage von 1850 an Waldböden ermittelten Wasser-Retentionskurven die Luftkapazität, die nutzbare Wasserspeicherkapazität und der Wassergehalt am permanenten Welkepunkt aus der Bodenart, der Bodendichte und dem C-Gehalt hergeleitet. Im Vergleich zu Ackerböden lagen die berechneten Luftkapazitäten aufgrund der unterschiedlichen vertikalen Verteilung der Bodendichten und Humusgehalte von Wald- und Ackerböden in Waldböden deutlich höher, Unterschiede in der nutzbaren Wasserspeicherkapazität hingegen waren gering. Die Ergebnisse zeigen, dass für Waldböden eine differenziertere Unterteilung der Dichteklassen notwendig ist, um die große Streuung im Bereich der unteren Bodendichte adäquat zu berücksichtigen. Andererseits basiert in Deutschland die Abschätzung physikalischer Bodeneigenschaften auf einer detaillierten Einteilung von 31 Texturklassen (Kartieranleitung und Forstliche Standortaufnahme). Da die Unterschiede zwischen vielen Texturklassen häufig sehr gering und statistisch nicht zu trennen sind, wurde unser Datensatz mit Hilfe einer Clusteranalyse auf 10 Texturklassen reduziert. Für diese Texturklassen wurden, unterteilt in jeweils 5 Dichteklassen, die Luftkapazitäten, die nutzbaren Wasserspeicherkapazitäten und der permanente Welkepunkt sowie die van Genuchten Parameter , r, , s, ,, und n berechnet. In einem zweiten Ansatz wurde eine Abschätzung dieser Kenngrößen mit Hilfe der multiplen Regression vorgenommen. [source]

The detailed forms of the LMC Cepheid PL and PLC relations

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2007
C. Koen
ABSTRACT Possible deviations from linearity of the Large Magellanic Cloud Cepheid period,luminosity (PL) and period,luminosity,colour (PLC) relations are investigated. Two data sets are studied, respectively from the Optical Gravitational Lensing Experiment (OGLE) and MACHO projects. A non-parametric test, based on linear regression residuals, suggests that neither PL relation is linear. If colour dependence is allowed for, then the MACHO PL relation is found to deviate more significantly from the linear, while the OGLE PL relation is consistent with linearity. These findings are confirmed by fitting ,Generalized Additive Models' (non-parametric regression functions) to the two data sets. Colour dependence is shown to be non-linear in both data sets, distinctly so in the case of the MACHO Cepheids. It is also shown that there is interaction between the period and the colour functions in the MACHO data. [source]

Adaptive tests of regression functions via multiscale generalized likelihood ratios

THE CANADIAN JOURNAL OF STATISTICS, Issue 2 2003
Chunming M. Zhang
Abstract Many applications of nonparametric tests based on curve estimation involve selecting a smoothing parameter. The author proposes an adaptive test that combines several generalized likelihood ratio tests in order to get power performance nearly equal to whichever of the component tests is best. She derives the asymptotic joint distribution of the component tests and that of the proposed test under the null hypothesis. She also develops a simple method of selecting the smoothing parameters for the proposed test and presents two approximate methods for obtaining its P-value. Finally, she evaluates the proposed test through simulations and illustrates its application to a set of real data. Moult applications des tests non paramétriques basés sur l'estimation de courbes font intervenir un paramètre de lissage. L'auteure propose un test adaptatif qui allie plusieurs tests du rapport de vraisemblances généralisés et rivalise de puissance avec le meilleur d'entre eux. Elle détermine la loi asymptotique conjointe des tests individuels et celle du test global sous l'hypothèse nulle. Elle montre aussi comment sélectionner facilement les paramètres de lissage du test global et propose deux méthodes de calcul approché de son seuil. Elle examine en outre le comportement du test proposé par voie de simulations et en illustre l'emploi dans un cas concret [source]