Nonparametric Statistics for Stochastic Processes

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.
• 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.
• 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.
• 5. Regression estimation and prediction in continuous time.
• 1. The kernel regression estimator in continuous time.
• 3. Superoptimal asymptotic quadratic error.
• 4. Limit in distribution.
• 5. Uniform convergence rates.
• 6. Sampling.
• 7. Nonparametric prediction in continuous time.
• Appendix—Numerical results.