Nonparametric Statistics for Stochastic Processes Estimation and Prediction
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1996, 1996
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| Edition: | 1st ed. 1996 |
| Series: | Lecture Notes in Statistics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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