Odile Pons 
FUNCTION ESTIM DENSITY.. (2ND ED) 

Nonparametric kernel estimators apply to the statistical analysis of independent or dependent sequences of random variables and for samples of continuous or discrete processes. The optimization of these procedures is based on the choice of a bandwidth that minimizes an estimation error and the weak convergence of the estimators is proved. This book introduces new mathematical results on statistical methods for the density and regression functions presented in the mathematical literature and for functions defining more complex models such as the models for the intensity of point processes, for the drift and variance of auto-regressive diffusions and the single-index regression models.

This second edition presents minimax properties with Lp risks, for a real p larger than one, and optimal convergence results for new kernel estimators of function defining processes: models for multidimensional variables, periodic intensities, estimators of the distribution functions of censored and truncated variables, estimation in frailty models, estimators for time dependent diffusions, for spatial diffusions and for diffusions with stochastic volatility.

Contents:

• Preface of the Second Edition


• Preface of the First Edition


• About the Author


• Introduction


• Kernel Estimator of a Density


• Kernel Estimator of a Regression Function


• Limits for the Varying Bandwidth Estimators


• Nonparametric Estimation of Quantiles


• Nonparametric Estimation of Intensities for Stochastic Processes


• Estimation in Semi-parametric Regression Models


• Diffusion Processes


• Applications to Time Series


• Appendix


• Notations


• Bibliography


• Index

Readership: Advanced undergraduate and graduate students in mathematical statistics and computational statistics; researchers and statisticians interested in the theory or applications to data analysis.

Review of the First Edition: This book is useful for researchers interested in the study of asymptotic properties of different types of optimum estimators obtained through the method of kernels. – Mathematical Reviews

Key Features:

• The book covers the theory of nonparametric estimation in several general models


• The second edition provides several new kernel estimators and their optimal properties