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Author: Odile Pons
Publisher: World Scientific
ISBN: 9814460613
Category : Mathematics
Languages : en
Pages : 212
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Book Description
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. Contents:IntroductionKernel Estimator of a DensityKernel Estimator of a Regression FunctionLimits for the Varying Bandwidths EstimatorsNonparametric Estimation of QuantilesNonparametric Estimation of Intensities for Stochastic ProcessesEstimation in Semi-Parametric Regression ModelsDiffusion ProcessesApplications to Time Series Readership: Advanced undergraduate and graduate students in mathematical statistics and computational statistics; researchers in mathematical or applied statistics; statisticians. Keywords:Kernel Estimation;Density;Regression;Intensity;Diffusion;Nonparametric;Weak Convergence;Ergodic Process;Intensity of Point Process;Kernel Estimation;Single-Index Models;Functional Time Series;Variable BandwidthKey Features:Covers a wide range of nonparametric models and presents new functional estimatorsContains a detailed presentation of the mathematical techniques for functional estimation with recent advances in their optimizationA valuable resource for scientific researchers who model observation dataReviews: “This book is useful for researchers interested in the study of asymptotic properties of different types of optimum estimators obtained through the method of kernels.” Mathematical Reviews
Author: Odile Pons
Publisher: World Scientific
ISBN: 9814460613
Category : Mathematics
Languages : en
Pages : 212
Get Book
Book Description
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. Contents:IntroductionKernel Estimator of a DensityKernel Estimator of a Regression FunctionLimits for the Varying Bandwidths EstimatorsNonparametric Estimation of QuantilesNonparametric Estimation of Intensities for Stochastic ProcessesEstimation in Semi-Parametric Regression ModelsDiffusion ProcessesApplications to Time Series Readership: Advanced undergraduate and graduate students in mathematical statistics and computational statistics; researchers in mathematical or applied statistics; statisticians. Keywords:Kernel Estimation;Density;Regression;Intensity;Diffusion;Nonparametric;Weak Convergence;Ergodic Process;Intensity of Point Process;Kernel Estimation;Single-Index Models;Functional Time Series;Variable BandwidthKey Features:Covers a wide range of nonparametric models and presents new functional estimatorsContains a detailed presentation of the mathematical techniques for functional estimation with recent advances in their optimizationA valuable resource for scientific researchers who model observation dataReviews: “This book is useful for researchers interested in the study of asymptotic properties of different types of optimum estimators obtained through the method of kernels.” Mathematical Reviews
Author: Odile Pons
Publisher: World Scientific
ISBN: 9811272859
Category : Mathematics
Languages : en
Pages : 259
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Book Description
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: George Roussas
Publisher: Springer Science & Business Media
ISBN: 9780792312260
Category : Mathematics
Languages : en
Pages : 732
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Book Description
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:
Publisher:
ISBN:
Category :
Languages : en
Pages : 148
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Book Description
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.
Author: Jian Qing Shi
Publisher: CRC Press
ISBN: 1439837732
Category : Mathematics
Languages : en
Pages : 218
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Book Description
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.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 148
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Book Description
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.
Author: B. L. S. Prakasa Rao
Publisher: Academic Press
ISBN: 148326923X
Category : Mathematics
Languages : en
Pages : 538
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Book Description
Nonparametric Functional Estimation is a compendium of papers, written by experts, in the area of nonparametric functional estimation. This book attempts to be exhaustive in nature and is written both for specialists in the area as well as for students of statistics taking courses at the postgraduate level. The main emphasis throughout the book is on the discussion of several methods of estimation and on the study of their large sample properties. Chapters are devoted to topics on estimation of density and related functions, the application of density estimation to classification problems, and the different facets of estimation of distribution functions. Statisticians and students of statistics and engineering will find the text very useful.
Author: Michael Panik
Publisher: CRC Press
ISBN: 1420091980
Category : Mathematics
Languages : en
Pages : 830
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Book Description
Regression Modeling: Methods, Theory, and Computation with SAS provides an introduction to a diverse assortment of regression techniques using SAS to solve a wide variety of regression problems. The author fully documents the SAS programs and thoroughly explains the output produced by the programs. The text presents the popular ordinary least squares (OLS) approach before introducing many alternative regression methods. It covers nonparametric regression, logistic regression (including Poisson regression), Bayesian regression, robust regression, fuzzy regression, random coefficients regression, L1 and q-quantile regression, regression in a spatial domain, ridge regression, semiparametric regression, nonlinear least squares, and time-series regression issues. For most of the regression methods, the author includes SAS procedure code, enabling readers to promptly perform their own regression runs. A Comprehensive, Accessible Source on Regression Methodology and Modeling Requiring only basic knowledge of statistics and calculus, this book discusses how to use regression analysis for decision making and problem solving. It shows readers the power and diversity of regression techniques without overwhelming them with calculations.
Author: Sam Efromovich
Publisher: Springer Science & Business Media
ISBN: 0387226389
Category : Mathematics
Languages : en
Pages : 414
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Book Description
This book gives a systematic, comprehensive, and unified account of modern nonparametric statistics of density estimation, nonparametric regression, filtering signals, and time series analysis. The companion software package, available over the Internet, brings all of the discussed topics into the realm of interactive research. Virtually every claim and development mentioned in the book is illustrated with graphs which are available for the reader to reproduce and modify, making the material fully transparent and allowing for complete interactivity.
Author: Bernard. W. Silverman
Publisher: CRC Press
ISBN: 9780412246203
Category : Mathematics
Languages : en
Pages : 190
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Book Description
Although there has been a surge of interest in density estimation in recent years, much of the published research has been concerned with purely technical matters with insufficient emphasis given to the technique's practical value. Furthermore, the subject has been rather inaccessible to the general statistician. The account presented in this book places emphasis on topics of methodological importance, in the hope that this will facilitate broader practical application of density estimation and also encourage research into relevant theoretical work. The book also provides an introduction to the subject for those with general interests in statistics. The important role of density estimation as a graphical technique is reflected by the inclusion of more than 50 graphs and figures throughout the text. Several contexts in which density estimation can be used are discussed, including the exploration and presentation of data, nonparametric discriminant analysis, cluster analysis, simulation and the bootstrap, bump hunting, projection pursuit, and the estimation of hazard rates and other quantities that depend on the density. This book includes general survey of methods available for density estimation. The Kernel method, both for univariate and multivariate data, is discussed in detail, with particular emphasis on ways of deciding how much to smooth and on computation aspects. Attention is also given to adaptive methods, which smooth to a greater degree in the tails of the distribution, and to methods based on the idea of penalized likelihood.
