This book deals with parametric and nonparametric density estimation from the maximum (penalized) likelihood point of view, including estimation under constraints. The focal points are existence and uniqueness of the estimators, almost sure convergence rates for the L1 error, and data-driven smoothing parameter selection methods, including their practical performance. The reader will gain insight into technical tools from probability theory and applied mathematics.

Inhalt

Parametric Maximum Likelihood Estimation Parametric Maximum Likelihood Estimation in Action Kernel Density Estimation Maximum Likelihood Density Estimation Monotone and Unimodal Densities Choosing the Smoothing Parameter Nonparametric Density Estimation in Action Convex Minimization in Finite Dimensional Spaces Convex Minimization in Infinite Dimensional Spaces * Convexity in Action