Alvo M., Yu P.L.H. A Parametric Approach to Nonparametric Statistics

Springer, 2018. — 277 p. — (Series in the Data Sciences). — ISBN: 3319941526.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.Fundamental Concepts in Parametric Inference
Tools for Nonparametric Statistics
Smooth Goodness of Fit Tests
One-Sample and Two-Sample Problems
Multi-Sample Problems
Tests for Trend and Association
Optimal Rank Tests
Efficiency
Multiple Change-Point Problems
Bayesian Models for Ranking Data
Analysis of Censored Data