Pons O. Functional Estimation for Density, Regression Models and Processes

World Scientific Publishing Company – 2011, 212 pages
ISBN: 9814343730, 9789814343732This 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 expounds on the construction of estimators for functionals of processes and densities, and provides asymptotic expansions and optimality properties from smooth estimators.
It also presents new regular estimators for functionals of processes, compares histogram and kernel estimators, compares several new estimators for single-index models, and it examines the weak convergence of the estimators.Kernel Estimator of a Density
Kernel Estimator of a Regression Function
Limits for the Varying Bandwidths Estimators
Nonparametric Estimation of Quantiles
Nonparametric Estimation of Intensities for Stochastic Processes
Estimation in Semi-Parametric Regression Models
Diffusion Processes
Applications to Time Series