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Functional Estimation For Density, Regression Models And Processes.
This book presents a unified approach on nonparametric estimators for models of independent observations, jump processes and continuous processes. New estimators are defined and their limiting behavior is studied. From a practical point of view, the book.
| Clasificación: | Libro Electrónico |
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| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
WSPC
2011.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; Contents; 1. Introduction; 1.1 Estimation of a density; 1.2 Estimation of a regression curve; 1.3 Estimation of functionals of processes; 1.4 Content of the book; 2. Kernel estimator of a density; 2.1 Introduction; 2.2 Risks and optimal bandwidths for the kernel estimator; 2.3 Weak convergence; 2.4 Minimax and histogram estimators; 2.5 Estimation of functionals of a density; 2.6 Density of absolutely continuous distributions; 2.7 Hellinger distance between a density and its estimator; 2.8 Estimation of the density under right-censoring.
- 2.9 Estimation of the density of left-censored variables2.10 Kernel estimator for the density of a process; 2.11 Exercises; 3. Kernel estimator of a regression function; 3.1 Introduction and notation; 3.2 Risks and convergence rates for the estimator; 3.3 Optimal bandwidths; 3.4 Weak convergence of the estimator; 3.5 Estimation of a regression curve by local polynomials; 3.6 Estimation in regression models with functional variance; 3.7 Estimation of the mode of a regression function; 3.8 Estimation of a regression function under censoring; 3.9 Proportional odds model.
- 3.10 Estimation for the regression function of processes3.11 Exercises; 4. Limits for the varying bandwidths estimators; 4.1 Introduction; 4.2 Estimation of densities; 4.3 Estimation of regression functions; 4.4 Estimation for processes; 4.5 Exercises; 5. Nonparametric estimation of quantiles; 5.1 Introduction; 5.2 Asymptotics for the quantile processes; 5.3 Bandwidth selection; 5.4 Estimation of the conditional density of Y given X; 5.5 Estimation of conditional quantiles for processes; 5.6 Inverse of a regression function; 5.7 Quantile function of right-censored variables.
- 5.8 Conditional quantiles with variable bandwidth5.9 Exercises; 6. Nonparametric estimation of intensities for stochastic processes; 6.1 Introduction; 6.2 Risks and convergences for estimators of the intensity; 6.2.1 Kernel estimator of the intensity; 6.2.2 Histogram estimator of the intensity; 6.3 Risks and convergences for multiplicative intensities; 6.3.1 Models with nonparametric regression functions; 6.3.2 Models with parametric regression functions; 6.4 Histograms for intensity and regression functions; 6.5 Estimation of the density of duration excess.
- 6.6 Estimators for processes on increasing intervals6.7 Models with varying intensity or regression coefficients; 6.8 Progressive censoring of a random time sequence; 6.9 Exercises; 7. Estimation in semi-parametric regression models; 7.1 Introduction; 7.2 Convergence of the estimators; 7.3 Nonparametric regression with a change of variables; 7.4 Exercises; 8. Diffusion processes; 8.1 Introduction; 8.2 Estimation for continuous diffusions by discretization; 8.3 Estimation for continuous diff usion processes; 8.4 Estimation of discretely observed diffusions with jumps.