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What Does Optimal Bandwidth Selection Mean For Nonparametric Regression Estimation
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Book Synopsis What Does Optimal Bandwidth Selection Mean for Nonparametric Regression Estimation? by : James Stephen Marron
Download or read book What Does Optimal Bandwidth Selection Mean for Nonparametric Regression Estimation? written by James Stephen Marron and published by . This book was released on 1986 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Bandwidth Selection in Nonparametric Regression Function Estimation by : Wolfgang Härdle
Download or read book Optimal Bandwidth Selection in Nonparametric Regression Function Estimation written by Wolfgang Härdle and published by . This book was released on 1983 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On Nonparametric Estimation and Inference with Censored Data, Bandwidth Selection for Local Polynomial Regression, and Subset Selection in Explanatory Regression Analyses by : Derick Randall Peterson
Download or read book On Nonparametric Estimation and Inference with Censored Data, Bandwidth Selection for Local Polynomial Regression, and Subset Selection in Explanatory Regression Analyses written by Derick Randall Peterson and published by . This book was released on 1998 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonparametric Functional Estimation and Related Topics by : G.G Roussas
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.
Book Synopsis Applied Nonparametric Regression by : Wolfgang Härdle
Download or read book Applied Nonparametric Regression written by Wolfgang Härdle and published by Cambridge University Press. This book was released on 1990 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to bring together in one place the techniques for regression curve smoothing involving more than one variable.
Book Synopsis Optimal Bandwidth Selection for Fitting an Additive Model by Local Polynomial Regression by : Jean-Didier Opsomer
Download or read book Optimal Bandwidth Selection for Fitting an Additive Model by Local Polynomial Regression written by Jean-Didier Opsomer and published by . This book was released on 1995 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Bandwidth Choice for Interval Estimation in GMM Regression by : Yixiao Sun
Download or read book Optimal Bandwidth Choice for Interval Estimation in GMM Regression written by Yixiao Sun and published by . This book was released on 2008 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: In time series regression with nonparametrically autocorrelated errors, it is now standard empirical practice to construct confidence intervals for regression coefficients on the basis of nonparametrically studentized t-statistics. The standard error used in the studentization is typically estimated by a kernel method that involves some smoothing process over the sample autocovariances. The underlying parameter (M) that controls this tuning process is a bandwidth or truncation lag and it plays a key role in the finite sample properties of tests and the actual coverage properties of the associated confidence intervals. The present paper develops a bandwidth choice rule for M that optimizes the coverage accuracy of interval estimators in the context of linear GMM regression. The optimal bandwidth balances the asymptotic variance with the asymptotic bias of the robust standard error estimator. This approach contrasts with the conventional bandwidth choice rule for nonparametric estimation where the focus is the nonparametric quantity itself and the choice rule balances asymptotic variance with squared asymptotic bias. It turns out that the optimal bandwidth for interval estimation has a different expansion rate and is typically substantially larger than the optimal bandwidth for point estimation of the standard errors. The new approach to bandwidth choice calls for refined asymptotic measurement of the coverage probabilities, which are provided by means of an Edgeworth expansion of the finite sample distribution of the nonparametrically studentized t-statistic. This asymptotic expansion extends earlier work and is of independent interest. A simple plug-in procedure for implementing this optimal bandwidth is suggested and simulations confirm that the new plug-in procedure works well in finite samples. Issues of interval length and false coverage probability are also considered, leading to a secondary approach to bandwidth selection with similar properties.
Book Synopsis Approximations to the Mean Integrated Squared Error with Applications to Optimal Bandwidth Selection for Nonparametric Regression Function Estimators by : Wolfgang Härdle
Download or read book Approximations to the Mean Integrated Squared Error with Applications to Optimal Bandwidth Selection for Nonparametric Regression Function Estimators written by Wolfgang Härdle and published by . This book was released on 1983 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Kernel Smoothing written by M.P. Wand and published by CRC Press. This book was released on 1994-12-01 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kernel smoothing refers to a general methodology for recovery of underlying structure in data sets. The basic principle is that local averaging or smoothing is performed with respect to a kernel function. This book provides uninitiated readers with a feeling for the principles, applications, and analysis of kernel smoothers. This is facilitated by the authors' focus on the simplest settings, namely density estimation and nonparametric regression. They pay particular attention to the problem of choosing the smoothing parameter of a kernel smoother, and also treat the multivariate case in detail. Kernal Smoothing is self-contained and assumes only a basic knowledge of statistics, calculus, and matrix algebra. It is an invaluable introduction to the main ideas of kernel estimation for students and researchers from other discipline and provides a comprehensive reference for those familiar with the topic.
Book Synopsis Automatic Bandwidth Selection and Data-driven Estimators in a Semiparametric Regression Model by : Sheng-Yan Hong
Download or read book Automatic Bandwidth Selection and Data-driven Estimators in a Semiparametric Regression Model written by Sheng-Yan Hong and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Consider the semiparametric regression model $y = x\sp{\tau}\beta + g(t) + e$ where x and t are covariates, $\beta$ is a p-vector of unknown parameters, g is an unknown smooth function, and e is the error term with mean 0 and variance $\sigma\sp2 > 0.$ This model arises naturally in situations where some covariates are difficult to be formulated into the model in a parametric fashion. There have been several approaches to estimating the parameter of interest $\beta$, all depending on some kinds of smoothing parameters inherent in the treatment of the nonparametric component g. For example, the kernel smoothing estimator $\ \beta\sb{2h}$, proposed in Speckman (1988), depends on the bandwidth h. So we face the important issue of how to choose those smoothing parameters. Although this issue has been extensively studied in the context of non-parametric regression, there has been little work on this semiparametric setting. In this thesis, we investigate asymptotic properties of the automatic bandwidth choice $\ h$ and the resulting data-driven kernel smoothing estimator $\ \beta\sb{2\ h}$ of the parameter $\beta.$ The bandwidth $\ h$ is chosen to minimize a general data-driven bandwidth selector which includes such traditional methods as Mallow's $C\sb{L}$ criterion, CV and GCV. Asymptotic optimality of $\ h$ is proved and its asymptotic normality is established. The data-driven estimator $\ \beta\sb{2\ h}$ is shown to be $\sqrt{n}$-consistent by establishing an asymptotic normality. We further study the accuracy of this normal approximation and show that, contrary to what might be expected, it can not attain the optimal Berry-Esseen rate $n\sp{-1/2}.$ Consequently, the one-sided confidence interval of $\beta$ based on this normal approximation is not first order accurate, causing potential poor coverage of the true parameter. To overcome this drawback, an estimator is proposed to reduce the bias of $\ \beta\sb{2h}.$ The data-driven version of the proposed estimator successfully attains the optimal normal approximation rate $n\sp{-1/2}.$ The corresponding one-sided confidence interval of $\beta$ is thus first order accurate. Simulation studies show that not only does the proposed estimator provide smaller bias and more accurate confidence interval in terms of coverage, as expected by our theoretical results, it also has better control of variance than $\ \beta\sb{2h}$ for both deterministic and automatic bandwidth choices.
Book Synopsis Semiparametric and Nonparametric Econometrics by : Aman Ullah
Download or read book Semiparametric and Nonparametric Econometrics written by Aman Ullah and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last three decades much research in empirical and theoretical economics has been carried on under various assumptions. For example a parametric functional form of the regression model, the heteroskedasticity, and the autocorrelation is always as sumed, usually linear. Also, the errors are assumed to follow certain parametric distri butions, often normal. A disadvantage of parametric econometrics based on these assumptions is that it may not be robust to the slight data inconsistency with the particular parametric specification. Indeed any misspecification in the functional form may lead to erroneous conclusions. In view of these problems, recently there has been significant interest in 'the semiparametric/nonparametric approaches to econometrics. The semiparametric approach considers econometric models where one component has a parametric and the other, which is unknown, a nonparametric specification (Manski 1984 and Horowitz and Neumann 1987, among others). The purely non parametric approach, on the other hand, does not specify any component of the model a priori. The main ingredient of this approach is the data based estimation of the unknown joint density due to Rosenblatt (1956). Since then, especially in the last decade, a vast amount of literature has appeared on nonparametric estimation in statistics journals. However, this literature is mostly highly technical and this may partly be the reason why very little is known about it in econometrics, although see Bierens (1987) and Ullah (1988).
Book Synopsis Principles of Nonparametric Learning by : Laszlo Györfi
Download or read book Principles of Nonparametric Learning written by Laszlo Györfi and published by Springer. This book was released on 2014-05-04 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a systematic in-depth analysis of nonparametric learning. It covers the theoretical limits and the asymptotical optimal algorithms and estimates, such as pattern recognition, nonparametric regression estimation, universal prediction, vector quantization, distribution and density estimation, and genetic programming.
Book Synopsis Nonparametric Econometrics by : Qi Li
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.
Book Synopsis Variance Estimation for Nonparametric Regression and Its Applications by : Mihails Levins
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:
Book Synopsis A Distribution-Free Theory of Nonparametric Regression by : László Györfi
Download or read book A Distribution-Free Theory of Nonparametric Regression written by László Györfi and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic in-depth analysis of nonparametric regression with random design. It covers almost all known estimates. The emphasis is on distribution-free properties of the estimates.
Book Synopsis Kernel Smoothing by : Sucharita Ghosh
Download or read book Kernel Smoothing written by Sucharita Ghosh and published by John Wiley & Sons. This book was released on 2018-01-09 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive theoretical overview of kernel smoothing methods with motivating examples Kernel smoothing is a flexible nonparametric curve estimation method that is applicable when parametric descriptions of the data are not sufficiently adequate. This book explores theory and methods of kernel smoothing in a variety of contexts, considering independent and correlated data e.g. with short-memory and long-memory correlations, as well as non-Gaussian data that are transformations of latent Gaussian processes. These types of data occur in many fields of research, e.g. the natural and the environmental sciences, and others. Nonparametric density estimation, nonparametric and semiparametric regression, trend and surface estimation in particular for time series and spatial data and other topics such as rapid change points, robustness etc. are introduced alongside a study of their theoretical properties and optimality issues, such as consistency and bandwidth selection. Addressing a variety of topics, Kernel Smoothing: Principles, Methods and Applications offers a user-friendly presentation of the mathematical content so that the reader can directly implement the formulas using any appropriate software. The overall aim of the book is to describe the methods and their theoretical backgrounds, while maintaining an analytically simple approach and including motivating examples—making it extremely useful in many sciences such as geophysics, climate research, forestry, ecology, and other natural and life sciences, as well as in finance, sociology, and engineering. A simple and analytical description of kernel smoothing methods in various contexts Presents the basics as well as new developments Includes simulated and real data examples Kernel Smoothing: Principles, Methods and Applications is a textbook for senior undergraduate and graduate students in statistics, as well as a reference book for applied statisticians and advanced researchers.
Book Synopsis Computer Intensive Methods in Statistics by : Wolfgang Härdle
Download or read book Computer Intensive Methods in Statistics written by Wolfgang Härdle and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The computer has created new fields in statistic. Numerical and statistical problems that were untackable five to ten years ago can now be computed even on portable personal computers. A computer intensive task is for example the numerical calculation of posterior distributions in Bayesian analysis. The Bootstrap and image analysis are two other fields spawned by the almost unlimited computing power. It is not only the computing power through that has revolutionized statistics, the graphical interactiveness on modern statistical environments has given us the possibility for deeper insight into our data. On November 21,22 1991 a conference on computer Intensive Methods in Statistics has been organized at the Universite Catholique de Louvain, Louvain-La-Neuve, Belgium. The organizers were Jan Beirlant (Katholieke Universiteit Leuven), Wolfgang Hardie (Humboldt-Universitat zu Berlin) and Leopold Simar (Universite Catholique de Louvain and Facultes Universitaires Saint-Louis). The meeting was the Xllth in the series of the Rencontre Franco-Beige des Statisticians. Following this tradition both theoretical statistical results and practical contributions of this active field of statistical research were presented. The four topics that have been treated in more detail were: Bayesian Computing; Interfacing Statistics and Computers; Image Analysis; Resampling Methods. Selected and refereed papers have been edited and collected for this book. 1) Bayesian Computing.
