Nonparametric Statistics for Stochastic Processes
Estimation and Prediction
Published on 27. March 1996
Book
Paperback/Softback
188 pages
978-0-387-94713-6 (ISBN)
Description
This book provides a mathematically rigorous treatment of the theory of nonparametric estimation and prediction for stochastic processes. It discusses discrete time and continuous time, and the emphasis is on the kernel methods. Several new results are presented concerning optimal and superoptimal convergence rates. How to implement the method is discussed in detail and several numerical results are presented. This book will be of interest to specialists in mathematical statistics and to those who wish to apply these methods to practical problems involving time series analysis.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1996
Language
English
Place of publication
NY
United States
Target group
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
1 farbige Abbildung
black & white illustrations
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Thickness: 10 mm
Weight
293 gr
ISBN-13
978-0-387-94713-6 (9780387947136)
DOI
10.1007/978-1-4684-0489-0
Schweitzer Classification
Other editions
New editions
Book
08/1998
2nd Edition
Springer
€149.79
Shipment within 5-7 days
Content
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.