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Download or read book Variance function estimation in nonparametric regression model written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Variance function estimation in nonparametric regression model.
Author : Mihails Levins
Publisher :
ISBN 13 :
Total Pages : 93 pages
Book Rating : 4.:/5 (244 download)
Download or read book Variance Estimation for Nonparametric Regression and Its Applications written by Mihails Levins and published by . This book was released on 2003 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter Hall
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (227 download)
Download or read book Variance Function Estimation in Regression: The Effect of Estimating the Mean written by Peter Hall and published by . This book was released on 1988 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider estimation of a variance function g in regression problems. Such estimation requires simultaneous estimation of the mean function f. We obtain sharp results on the extent to which the smoothness of f influences best rates of convergence for estimating g. For example, in nonparametric regression with two derivatives on g, classical rates of convergence are possible if and only if the unknown f satisfies a Lipschitz condition of order 1/3 or more. If a parametric model is known for g, then g may be estimated n 1/2 - consistently if and only if f is Lipschitz of order 1/2 or more. Optimal rates of convergence are attained by kernel estimators. (kr).
Author : Jia Liang
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (122 download)
Download or read book Adequacy Checking for the Variance Function in Nonparametric Regression written by Jia Liang and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Correctly specifying the parametric form of the variance function in regression models can help us make more efficient statistical inferences. Many existing Lack-of-fit testing procedures have already been proposed to decide the proper forms of the variance function, however, most of them are either checking the homoscedasticity, that is, to see if the variance function is a constant, or checking a pre-specified parametric forms of the variance function under the assumption of the mean regression function being known. In this report, we would like to construct some formal testing procedure to check the appropriateness of certain parametric forms for the variance function when the mean regression function is unknown. The report consists of two parts. In the first part, we propose a minimum distance-based test to check the forms of the variance function. The test statistics is a modified L2-distance between a nonparametric estimate and a parametric estimate of the variance function under the null hypothesis. The Nadaraya-Watson kernel regression function estimator is used to estimate the regression function. The large sample properties, including the consistency and asymptotic normality, of the minimum distance estimate for the parameters in the variance function are discussed; the asymptotic distribution of the test statistics under the null hypothesis is established, as well as the consistency of the test and the power under local alternative hypotheses. Simulation studies, comparison studies, as well as some applications to the real data sets, are carried out to evaluate the finite sample performance of the proposed test. In the second part, we proposed a computationally efficient test procedure for checking the parametric forms of the variance function. The test is based on an empirical smoothing of the fitted residuals by replacing the mean regression function with the Nadaraya-Watson estimator and a pre-obtained root-n consistent estimate of the parameter in the variance function. By multiplying the kernel density estimate at each individual sample points to the fitted residual, we successfully remove the constraint of compact support for design variables assumed in some existing work. Large sample properties of the proposed test under the null hypothesis is discussed alongside with consistency of the test and the power under local alternatives. Finally, some simulation studies are carried out showing the performance of the test under finite population.
Author : Odile Pons
Publisher : World Scientific
ISBN 13 : 9814343749
Total Pages : 210 pages
Book Rating : 4.8/5 (143 download)
Download or read book Functional Estimation for Density, Regression Models and Processes written by Odile Pons and published by World Scientific. This book was released on 2011 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified approach on nonparametric estimators for models of independent observations, jump processes and continuous processes. New estimators are defined and their limiting behavior is studied. From a practical point of view, the book
Author : D. Ruppert
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Local Polynomial Variance Function Estimation written by D. Ruppert and published by . This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focussed on local polynomial smoothers. Both the mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The effect of preliminary estimation of the mean is studied, and a "degrees of freedom" is proposed. The corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known. A proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions. The proposal is illustrated with data from the LIDAR method of measuring atmospheric pollutants and from turbulence model computations.
Author : Odile Pons
Publisher : World Scientific
ISBN 13 : 9811272859
Total Pages : 259 pages
Book Rating : 4.8/5 (112 download)
Download or read book Functional Estimation For Density, Regression Models And Processes (Second Edition) written by Odile Pons and published by World Scientific. This book was released on 2023-09-22 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonparametric kernel estimators apply to the statistical analysis of independent or dependent sequences of random variables and for samples of continuous or discrete processes. The optimization of these procedures is based on the choice of a bandwidth that minimizes an estimation error and the weak convergence of the estimators is proved. This book introduces new mathematical results on statistical methods for the density and regression functions presented in the mathematical literature and for functions defining more complex models such as the models for the intensity of point processes, for the drift and variance of auto-regressive diffusions and the single-index regression models.This second edition presents minimax properties with Lp risks, for a real p larger than one, and optimal convergence results for new kernel estimators of function defining processes: models for multidimensional variables, periodic intensities, estimators of the distribution functions of censored and truncated variables, estimation in frailty models, estimators for time dependent diffusions, for spatial diffusions and for diffusions with stochastic volatility.
Author : Qi Li
Publisher : Princeton University Press
ISBN 13 : 0691248087
Total Pages : 768 pages
Book Rating : 4.6/5 (912 download)
Download or read book Nonparametric Econometrics written by Qi Li and published by Princeton University Press. This book was released on 2023-07-18 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, up-to-date textbook on nonparametric methods for students and researchers Until now, students and researchers in nonparametric and semiparametric statistics and econometrics have had to turn to the latest journal articles to keep pace with these emerging methods of economic analysis. Nonparametric Econometrics fills a major gap by gathering together the most up-to-date theory and techniques and presenting them in a remarkably straightforward and accessible format. The empirical tests, data, and exercises included in this textbook help make it the ideal introduction for graduate students and an indispensable resource for researchers. Nonparametric and semiparametric methods have attracted a great deal of attention from statisticians in recent decades. While the majority of existing books on the subject operate from the presumption that the underlying data is strictly continuous in nature, more often than not social scientists deal with categorical data—nominal and ordinal—in applied settings. The conventional nonparametric approach to dealing with the presence of discrete variables is acknowledged to be unsatisfactory. This book is tailored to the needs of applied econometricians and social scientists. Qi Li and Jeffrey Racine emphasize nonparametric techniques suited to the rich array of data types—continuous, nominal, and ordinal—within one coherent framework. They also emphasize the properties of nonparametric estimators in the presence of potentially irrelevant variables. Nonparametric Econometrics covers all the material necessary to understand and apply nonparametric methods for real-world problems.
Author : Odile Pons
Publisher : World Scientific
ISBN 13 : 9814460613
Total Pages : 210 pages
Book Rating : 4.8/5 (144 download)
Download or read book Functional Estimation For Density, Regression Models And Processes written by Odile Pons and published by World Scientific. This book was released on 2011-03-21 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified approach on nonparametric estimators for models of independent observations, jump processes and continuous processes. New estimators are defined and their limiting behavior is studied. From a practical point of view, the book expounds on the construction of estimators for functionals of processes and densities, and provides asymptotic expansions and optimality properties from smooth estimators.It also presents new regular estimators for functionals of processes, compares histogram and kernel estimators, compares several new estimators for single-index models, and it examines the weak convergence of the estimators.
Author : Aggrey Adem
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659125133
Total Pages : 68 pages
Book Rating : 4.1/5 (251 download)
Download or read book Non Parametric Optimal Estimation of the Regression Function written by Aggrey Adem and published by LAP Lambert Academic Publishing. This book was released on 2012-05 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: One main function of statistical science is to demonstrate how valid inferences about some population may be made from an examination of the information provided by a sample or a set of a given data. To achieve this, an appropriate model exhibiting parsimony of parameters with a well-defined scope has to be selected. Once the desired model has been identified, there is a need to obtain precise estimate of all the parameters of the model before it is fitted. The problem of estimation is how to achieve the precision of the estimates. This can better be addressed by having an insight into approaches to estimation. The main approaches to estimation are parametric and non-parametric. In this project, proposed how to choose the weights such that the efficiency of the estimation is improved. We replaced the weights with the empirically estimated covariances. The non-parametrically estimated variance function will approximate the true variance function. Therefore, the estimating equations with the estimated variance function are expected to achieve the optimality in estimating the regression co-efficient in the absence of any knowledge regarding the true variance function.
Author : Sam Efromovich
Publisher : CRC Press
ISBN 13 : 135167983X
Total Pages : 867 pages
Book Rating : 4.3/5 (516 download)
Download or read book Missing and Modified Data in Nonparametric Estimation written by Sam Efromovich and published by CRC Press. This book was released on 2018-03-12 with total page 867 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic and unified approach for modern nonparametric treatment of missing and modified data via examples of density and hazard rate estimation, nonparametric regression, filtering signals, and time series analysis. All basic types of missing at random and not at random, biasing, truncation, censoring, and measurement errors are discussed, and their treatment is explained. Ten chapters of the book cover basic cases of direct data, biased data, nondestructive and destructive missing, survival data modified by truncation and censoring, missing survival data, stationary and nonstationary time series and processes, and ill-posed modifications. The coverage is suitable for self-study or a one-semester course for graduate students with a prerequisite of a standard course in introductory probability. Exercises of various levels of difficulty will be helpful for the instructor and self-study. The book is primarily about practically important small samples. It explains when consistent estimation is possible, and why in some cases missing data should be ignored and why others must be considered. If missing or data modification makes consistent estimation impossible, then the author explains what type of action is needed to restore the lost information. The book contains more than a hundred figures with simulated data that explain virtually every setting, claim, and development. The companion R software package allows the reader to verify, reproduce and modify every simulation and used estimators. This makes the material fully transparent and allows one to study it interactively. Sam Efromovich is the Endowed Professor of Mathematical Sciences and the Head of the Actuarial Program at the University of Texas at Dallas. He is well known for his work on the theory and application of nonparametric curve estimation and is the author of Nonparametric Curve Estimation: Methods, Theory, and Applications. Professor Sam Efromovich is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association.
Author : David Brian Holiday
Publisher :
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.:/5 (318 download)
Download or read book On Nonparametric Regression Estimation in a Correlated-errors Model written by David Brian Holiday and published by . This book was released on 1986 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (89 download)
Download or read book Kriging with Nonparametric Variance Function Estimation written by and published by . This book was released on 1998 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : G.G Roussas
Publisher : Springer Science & Business Media
ISBN 13 : 9401132224
Total Pages : 691 pages
Book Rating : 4.4/5 (11 download)
Download or read book Nonparametric Functional Estimation and Related Topics written by G.G Roussas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: About three years ago, an idea was discussed among some colleagues in the Division of Statistics at the University of California, Davis, as to the possibility of holding an international conference, focusing exclusively on nonparametric curve estimation. The fruition of this idea came about with the enthusiastic support of this project by Luc Devroye of McGill University, Canada, and Peter Robinson of the London School of Economics, UK. The response of colleagues, contacted to ascertain interest in participation in such a conference, was gratifying and made the effort involved worthwhile. Devroye and Robinson, together with this editor and George Metakides of the University of Patras, Greece and of the European Economic Communities, Brussels, formed the International Organizing Committee for a two week long Advanced Study Institute (ASI) sponsored by the Scientific Affairs Division of the North Atlantic Treaty Organization (NATO). The ASI was held on the Greek Island of Spetses between July 29 and August 10, 1990. Nonparametric functional estimation is a central topic in statistics, with applications in numerous substantive fields in mathematics, natural and social sciences, engineering and medicine. While there has been interest in nonparametric functional estimation for many years, this has grown of late, owing to increasing availability of large data sets and the ability to process them by means of improved computing facilities, along with the ability to display the results by means of sophisticated graphical procedures.
Author : Alexandre B. Tsybakov
Publisher : Springer Science & Business Media
ISBN 13 : 0387790527
Total Pages : 222 pages
Book Rating : 4.3/5 (877 download)
Download or read book Introduction to Nonparametric Estimation written by Alexandre B. Tsybakov and published by Springer Science & Business Media. This book was released on 2008-10-22 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from lecture notes and ready to be used for a course on the graduate level, this concise text aims to introduce the fundamental concepts of nonparametric estimation theory while maintaining the exposition suitable for a first approach in the field.
Author : Yousef Fayz M. Alharbi
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (858 download)
Download or read book Error Variance Estimation in Nonparametric Regression Models written by Yousef Fayz M. Alharbi and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we take a fresh look at the error variance estimation in nonparametric regression models. The requirement for a suitable estimator of error variance in nonparametric regression models is well known and hence several estimators are suggested in the literature. We review these estimators and classify them into two types. Of these two types, one is difference-based estimators, whereas the other is obtained by smoothing the residual squares. We propose a new class of estimators which, in contrast to the existing estimators, is obtained by smoothing the product of residual and response variable. The properties of the new estimator are then studied in the settings of homoscedastic (variance is a constant) and heteroscedastic (variance is a function of x ) nonparametric regression models. In the current thesis, definitions of the new error variance estimators are provided in these two different settings. For these two proposed estimators, we carry out the mean square analysis and we then find their MSE-optimal bandwidth. We also study the asymptotic behaviour of the proposed estimators and we show that the asymptotic distributions in both settings are asymptotically normal distributions. We then conduct simulation studies to exhibit their finite sample performances.
Author : Jonathan Alan Raz
Publisher :
ISBN 13 :
Total Pages : 306 pages
Book Rating : 4.:/5 (7 download)
Download or read book Testing for No Effect when Estimating a Smooth Function by Nonparametric Regression written by Jonathan Alan Raz and published by . This book was released on 1988 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
