This book is designed to bridge the gap between traditional textbooks in statistics and more advanced books that include the sophisticated nonparametric techniques. It covers topics in parametric and nonparametric large-sample estimation theory. The exposition is based on a collection of relatively simple statistical models. It gives a thorough mathematical analysis for each of them with all the rigorous proofs and explanations. The book also includes a number of helpful exercises. Prerequisites for the book include senior undergraduate/beginning graduate-level courses in probability and statistics.
Parametric models: The Fisher efficiency The Bayes and minimax estimators Asymptotic minimaxity Some irregular statistical experiments Change-point problem Sequential estimators Linear parametric regression Nonparametric regression: Estimation in nonparametric regression Local polynomial approximation of regression function Estimation of regression in global norms Estimation by splines Asymptotic optimality in global norms Estimation in nonparametric models: Estimation of functionals Dimension and structure in nonparametric regression Adaptive estimation Testing of nonparametric hypotheses Bibliography Index of notation Index