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Nonparametric Functional Estimation and Related Topics

Nonparametric Functional Estimation and Related Topics
Author: G.G Roussas
Publisher: Springer Science & Business Media
Total Pages: 691
Release: 2012-12-06
Genre: Mathematics
ISBN: 9401132224

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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.


Semiparametric and Nonparametric Econometrics

Semiparametric and Nonparametric Econometrics
Author: Aman Ullah
Publisher: Springer Science & Business Media
Total Pages: 180
Release: 2012-12-06
Genre: Business & Economics
ISBN: 3642518486

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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).


Functional Estimation For Density, Regression Models And Processes (Second Edition)

Functional Estimation For Density, Regression Models And Processes (Second Edition)
Author: Odile Pons
Publisher: World Scientific
Total Pages: 259
Release: 2023-09-22
Genre: Mathematics
ISBN: 9811272859

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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.


Nonparametric Regression and Spline Smoothing, Second Edition

Nonparametric Regression and Spline Smoothing, Second Edition
Author: Randall L. Eubank
Publisher: CRC Press
Total Pages: 368
Release: 1999-02-09
Genre: Mathematics
ISBN: 9780824793371

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Provides a unified account of the most popular approaches to nonparametric regression smoothing. This edition contains discussions of boundary corrections for trigonometric series estimators; detailed asymptotics for polynomial regression; testing goodness-of-fit; estimation in partially linear models; practical aspects, problems and methods for confidence intervals and bands; local polynomial regression; and form and asymptotic properties of linear smoothing splines.


Nonparametric Regression and Spline Smoothing

Nonparametric Regression and Spline Smoothing
Author: Randall L. Eubank
Publisher: CRC Press
Total Pages: 359
Release: 1999-02-09
Genre: Mathematics
ISBN: 1482273144

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Provides a unified account of the most popular approaches to nonparametric regression smoothing. This edition contains discussions of boundary corrections for trigonometric series estimators; detailed asymptotics for polynomial regression; testing goodness-of-fit; estimation in partially linear models; practical aspects, problems and methods for co