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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 comparaison with parametric ones, including numerical results. Many of the results pre sented here are new and have not yet been published, expecially those in Chapters N and V. I am grateful to W. HardIe, Y. Kutoyants, F. Merlevede and G. Oppen heim 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 acknowledgment also goes to M. Carbon, M. Delecroix, B. Milcamps and J .M. Poggi who authorized me to reproduce their numerical results.
Synopsis.- 1. The object of the study.- 2. The kernel density estimator.- 3. The kernel regression estimator and the induced predictor.- 4. Mixing processes.- 5. Density estimation.- 6. Regression estimation and Prediction.- 7. Implementation of nonparametric method.- 1. Inequalities for mixing processes.- 1. Mixing.- 2. Coupling.- 3. Inequalities for covariances and joint densities.- 4. Exponential type inequalities.- 5. Some limit theorems for strongly mixing processes.- Notes.- 2. Density estimation for discrete time processes.- 1. Density estimation.- 2. Optimal asymptotic quadratic error.- 3. Uniform almost sure convergence.- 4. Asymptotic normality.- 5. Non regular cases.- Notes.- 3. Regression estimation and prediction for discrete time processes.- 1. Regression estimation.- 2. Asymptotic behaviour of the regression estimator.- 3. Prediction for a stationary Markov process of order k.- 4. Prediction for general processes.- 5. Implementation of nonparametric method.- Notes.- 4. Density estimation for continuous time processes.- 1. The kernel density estimator in continuous time.- 2. Optimal and superoptimal asymptotic quadratic error.- 3. Optimal and superoptimal uniform convergence rates.- 4. Sampling.- Notes.- 5. Regression estimation and prediction in continuous time.- 1. The kernel regression estimator in continuous time.- 2. Optimal asymptotic quadratic error.- 3. Superoptimal asymptotic quadratic error.- 4. Limit in distribution.- 5. Uniform convergence rates.- 6. Sampling.- 7. Nonparametric prediction in continuous time.- Notes.- Appendix—Numerical results.