Nonparametric Statistics for Stochastic Processes

Recently new developments have taken place in the theory of nonpara metric statistics for stochastic processes. Optimal asymptotic results have been obtained and special behaviour of estimators and predictors in con tinuous time has been pointed out. This book is devoted to these questions. It also gives some indica tions about implementation of nonparametric methods and comparison with parametric ones, including numerical results. Ma.ny of the results presented here are new and have not yet been published, expecially those in Chapters IV, V and VI. Apart from some improvements and corrections, this second edition con tains a new chapter dealing with the use of local time in density estimation. I am grateful to W. Hardie, Y. Kutoyants, F. Merlevede and G. Oppenheim who made important remarks that helped much to improve the text. I am greatly indebted to B. Heliot for her careful reading of the manus cript which allowed to ameliorate my english. I also express my gratitude to D. Blanke, L. Cotto and P. Piacentini who read portions of the manuscript and made some useful suggestions. I also thank M. Gilchrist and J. Kimmel for their encouragements. My aknowlegment also goes to M. Carbon, M. Delecroix, B. Milcamps and J .M. Poggi who authorized me to reproduce their numerical results. My greatest debt is to D. Tilly who prepared the typescript with care and efficiency. Preface to the second edition This edition contains some improvements and corrections, and two new chapters.

Written by one of the leading statisticians in France, this revision offers new material on the theory and applications of nonparametric statistics for stochastic processes.

Synopsis.- 1. Inequalities for mixing processes.- 2. Density estimation for discrete time processes.- 3. Regression estimation and prediction for discrete time processes.- 4. Kernel density estimation for continuous time processes.- 5. Regression estimation and prediction in continuous time.- 6. The local time density estimator.- 7. Implementation of nonparametric method and numerical applications.- References.