Bosq Nonparametric Statistics for Stochastic Processes

Estimation and Prediction
Erscheinungsjahr 2012
ISBN: 978-1-4684-0489-0
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 110, eBook

Reihe: Lecture Notes in Statistics

Zielgruppe

Research

Autoren/Hrsg.

Bosq, Denis

Inhaltsverzeichnis

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.