Functional Estimation: The Asymptotic Regression Approach

Functional Estimation: The Asymptotic Regression Approach
Author:
Publisher:
Total Pages: 148
Release: 1998
Genre:
ISBN:

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Through an appeal to asymptotic Gaussian representations of certain empirical stochastic processes, we are able to apply the technique of continuous regression to derive parametric and nonparametric functional estimates for underlying probability laws. This asymptotic regression approach yields estimates for a wide range of statistical problems, including estimation based on the empirical quantile function, Poisson process intensity estimation, parametric and nonparametric density estimation, and estimation for inverse problems. Consistency and asymptotic distribution theory are established for the general parametric estimator. In the case of nonparametric estimation, we obtain rates of convergence for the density estimator in various norms. We demonstrate the application of this methodology to inverse problems and compare the performance of the asymptotic regression estimator to other estimation schemes in a simulation study. The asymptotic regression estimates are easily computable and are seen to be competitive with other results in these areas.

Functional Estimation: The Asymptotic Regression Approach

Functional Estimation: The Asymptotic Regression Approach
Author:
Publisher:
Total Pages: 148
Release: 1998
Genre:
ISBN:

Download Functional Estimation: The Asymptotic Regression Approach Book in PDF, Epub and Kindle

Through an appeal to asymptotic Gaussian representations of certain empirical stochastic processes, we are able to apply the technique of continuous regression to derive parametric and nonparametric functional estimates for underlying probability laws. This asymptotic regression approach yields estimates for a wide range of statistical problems, including estimation based on the empirical quantile function, Poisson process intensity estimation, parametric and nonparametric density estimation, and estimation for inverse problems. Consistency and asymptotic distribution theory are established for the general parametric estimator. In the case of nonparametric estimation, we obtain rates of convergence for the density estimator in various norms. We demonstrate the application of this methodology to inverse problems and compare the performance of the asymptotic regression estimator to other estimation schemes in a simulation study. The asymptotic regression estimates are easily computable and are seen to be competitive with other results in these areas.

Functional Estimation For Density, Regression Models And Processes

Functional Estimation For Density, Regression Models And Processes
Author: Odile Pons
Publisher: World Scientific
Total Pages: 210
Release: 2011-03-21
Genre: Mathematics
ISBN: 9814460613

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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.

Functional Estimation for Density, Regression Models and Processes

Functional Estimation for Density, Regression Models and Processes
Author: Odile Pons
Publisher: World Scientific
Total Pages: 210
Release: 2011
Genre: Mathematics
ISBN: 9814343749

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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

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 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.

Nonlinear Regression with R

Nonlinear Regression with R
Author: Christian Ritz
Publisher: Springer Science & Business Media
Total Pages: 151
Release: 2008-12-11
Genre: Mathematics
ISBN: 0387096167

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- Coherent and unified treatment of nonlinear regression with R. - Example-based approach. - Wide area of application.

Asymptotic Theory of Nonlinear Regression

Asymptotic Theory of Nonlinear Regression
Author: A.A. Ivanov
Publisher: Springer Science & Business Media
Total Pages: 333
Release: 2013-04-17
Genre: Mathematics
ISBN: 9401588775

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Let us assume that an observation Xi is a random variable (r.v.) with values in 1 1 (1R1 , 8 ) and distribution Pi (1R1 is the real line, and 8 is the cr-algebra of its Borel subsets). Let us also assume that the unknown distribution Pi belongs to a 1 certain parametric family {Pi() , () E e}. We call the triple £i = {1R1 , 8 , Pi(), () E e} a statistical experiment generated by the observation Xi. n We shall say that a statistical experiment £n = {lRn, 8 , P; ,() E e} is the product of the statistical experiments £i, i = 1, ... ,n if PO' = P () X ... X P () (IRn 1 n n is the n-dimensional Euclidean space, and 8 is the cr-algebra of its Borel subsets). In this manner the experiment £n is generated by n independent observations X = (X1, ... ,Xn). In this book we study the statistical experiments £n generated by observations of the form j = 1, ... ,n. (0.1) Xj = g(j, (}) + cj, c c In (0.1) g(j, (}) is a non-random function defined on e , where e is the closure in IRq of the open set e ~ IRq, and C j are independent r. v .-s with common distribution function (dJ.) P not depending on ().

Gaussian Process Regression Analysis for Functional Data

Gaussian Process Regression Analysis for Functional Data
Author: Jian Qing Shi
Publisher: CRC Press
Total Pages: 218
Release: 2011-07-01
Genre: Mathematics
ISBN: 1439837732

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Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables. Covering the basics of Gaussian process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dimensional data and variable selection. The remainder of the text explores advanced topics of functional regression analysis, including novel nonparametric statistical methods for curve prediction, curve clustering, functional ANOVA, and functional regression analysis of batch data, repeated curves, and non-Gaussian data. Many flexible models based on Gaussian processes provide efficient ways of model learning, interpreting model structure, and carrying out inference, particularly when dealing with large dimensional functional data. This book shows how to use these Gaussian process regression models in the analysis of functional data. Some MATLAB® and C codes are available on the first author’s website.