A Parametric Approach to Nonparametric Statistics

Description

This book demonstrates that nonparametric statistics can be taught from a parametric point of view. As a result, one can exploit various parametric tools such as the use of the likelihood function, penalized likelihood and score functions to not only derive well-known tests but to also go beyond and make use of Bayesian methods to analyze ranking data. The book bridges the gap between parametric and nonparametric statistics and presents the best practices of the former while enjoying the robustness properties of the latter. This book can be used in a graduate course in nonparametrics, with parts being accessible to senior undergraduates. In addition, the book will be of wide interest to statisticians and researchers in applied fields. Front Matter ....Pages i-xiv Front Matter ....Pages 1-1 Introduction (Mayer Alvo, Philip L. H. Yu)....Pages 3-4 Fundamental Concepts in Parametric Inference (Mayer Alvo, Philip L. H. Yu)....Pages 5-44 Tools for Nonparametric Statistics (Mayer Alvo, Philip L. H. Yu)....Pages 45-59 Front Matter ....Pages 61-61 Smooth Goodness of Fit Tests (Mayer Alvo, Philip L. H. Yu)....Pages 63-89 One-Sample and Two-Sample Problems (Mayer Alvo, Philip L. H. Yu)....Pages 91-115 Multi-Sample Problems (Mayer Alvo, Philip L. H. Yu)....Pages 117-135 Tests for Trend and Association (Mayer Alvo, Philip L. H. Yu)....Pages 137-161 Optimal Rank Tests (Mayer Alvo, Philip L. H. Yu)....Pages 163-186 Efficiency (Mayer Alvo, Philip L. H. Yu)....Pages 187-205 Front Matter ....Pages 207-207 Multiple Change-Point Problems (Mayer Alvo, Philip L. H. Yu)....Pages 209-227 Bayesian Models for Ranking Data (Mayer Alvo, Philip L. H. Yu)....Pages 229-243 Analysis of Censored Data (Mayer Alvo, Philip L. H. Yu)....Pages 245-256 Back Matter ....Pages 257-279