Nonparametric Statistics for Stochastic Processes: Estimation and Prediction

D. Bosq (auth.)9780387947136, 0387947132

This book is devoted to the theory and applications of nonparametic functional estimation and prediction. Chapter 1 provides an overview of inequalities and limit theorems for strong mixing processes. Density and regression estimation in discrete time are studied in Chapter 2 and 3. The special rates of convergence which appear in continuous time are presented in Chapters 4 and 5. This second edition is extensively revised and it contains two new chapters. Chapter 6 discusses the surprising local time density estimator. Chapter 7 gives a detailed account of implementation of nonparametric method and practical examples in economics, finance and physics. Comarison with ARMA and ARCH methods shows the efficiency of nonparametric forecasting. The prerequisite is a knowledge of classical probability theory and statistics. Denis Bosq is Professor of Statistics at the Unviersity of Paris 6 (Pierre et Marie Curie). He is Editor-in-Chief of “Statistical Inference for Stochastic Processes” and an editor of “Journal of Nonparametric Statistics”. He is an elected member of the International Statistical Institute. He has published about 90 papers or works in nonparametric statistics and four books.

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Table of contents :
Front Matter….Pages i-xvi
Synopsis….Pages 1-15
Inequalities for mixing processes….Pages 17-39
Density estimation for discrete time processes….Pages 41-65
Regression estimation and prediction for discrete time processes….Pages 67-87
Kernel density estimation for continuous time processes….Pages 89-128
Regression estimation and prediction in continuous time….Pages 129-144
The local time density estimator….Pages 145-167
Implementation of nonparametric method and numerical applications….Pages 169-195
Back Matter….Pages 197-212