Concepts of Nonparametric Theory

by J.W. Pratt, J.D. Gibbons

Overview

This book explores both non parametric and general statistical ideas by developing non parametric procedures in simple situations. The major goal is to give the reader a thorough intuitive understanding of the concepts underlying nonparametric procedures and a full appreciation of the properties and operating characteristics of those procedures covered. This book differs from most statistics books by including considerable philosophical and methodological discussion. Special attention is given to discussion of the strengths and weaknesses of various statistical methods and approaches. Difficulties that often arise in applying statistical theory to real data also receive substantial attention. The approach throughout is more conceptual than mathematical. The "Theorem-Proof" format is avoided; generally, properties are "shown," rather than "proved." In most cases the ideas behind the proof of an im­ portant result are discussed intuitively in the text and formal details are left as an exercise for the reader. We feel that the reader will learn more from working such things out than from checking step-by-step a complete presentation of all details.

Product Details

ISBN-13:	9781461259336
Publisher:	Springer New York
Publication date:	02/10/2012
Series:	Springer Series in Statistics
Edition description:	Softcover reprint of the original 1st ed. 1981
Pages:	462
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

1 Concepts of Statistical Inference and the Binomial Distribution.- 1 Introduction.- 2 Probability Distributions.- 3 Estimators and their Properties.- 4 Hypothesis Testing.- 5 Randomized Test Procedures.- 6 Confidence Regions.- 7 Properties of One-Tailed Procedures.- 8 Choice of Two-Tailed Procedures and their Properties.- 9 Appendices to Chapter 1.- Problems.- 2 One-Sample and Paired-Sample Inferences Based on the Binomial Distribution.- 1 Introduction.- 2 Quantile Values.- 3 The One-Sample Sign Test for Quantile Values.- 4 Confidence Procedures Based on the Sign Test.- 5 Interpolation between Attainable Levels.- 6 The Sign Test with Zero Differences.- 7 Paired Observations.- 8 Comparing Proportions using Paired Observations.- 9 Tolerance Regions.- Problems.- 3 One-Sample and Paired-Sample Inferences Based on Signed Ranks.- 1 Introduction.- 2 The Symmetry Assumption or Hypothesis.- 3 The Wilcoxon Signed-Rank Test.- 4 Confidence Procedures Based on the Wilcoxon Signed-Rank Test.- 5 A Modified Wilcoxon Procedure.- 6 Zeros and Ties.- 7 Other Signed-Rank Procedures.- 8 Invariance and Signed-Rank Procedures.- 9 Locally Most Powerful Signed-Rank Tests 181 Problems.- 4 One-Sample and Paired-Sample Inferences Based on the Method of Randomization.- 1 Introduction.- 2 Randomization Procedures Based on the Sample Mean and Equivalent Criteria.- 3 The General Class of One-Sample Randomization Tests.- 4 Most Powerful Randomization Tests.- 5 Obervation-Randomization versus Rank-Randomization Tests.- Problems.- 5 Two-Sample Rank Procedures for Location.- 1 Introduction.- 2 The Shift Assumption.- 3 The Median Test, Other Two-Sample Sign Tests, and Related Confidence Procedures.- 4 Procedures Based on Sums of Ranks.- 5 Procedures Based on Sums of Scores.- 6 Two-Sample Rank Tests and theY — X Differences.- 7 Invariance and Two-Sample Rank Procedures.- 8 Locally Most Powerful Rank Tests.- Problems.- 6 Two-Sample Inferences Based on the Method of Randomization.- 1 Introduction.- 2 Randomization Procedures Based on the Difference Between Sample Means and Equivalent Criteria.- 3 The Class of Two-Sample Randomization Tests.- 4 Most Powerful Randomization Tests.- Problems.- 7 Kolmogorov-Smirnov Two-Sample Tests.- 1 Introduction.- 2 Empirical Distribution Function.- 3 Two-Sample Kolmogorov-Smirnov Statistics.- 4 Null Distribution Theory.- 5 Ties.- 6 Performance.- 7 One-Sample Kolmogorov-Smirnov Statistics.- Problems.- 8 Asymptotic Relative Efficiency.- 1 Introduction.- 2 Asymptotic Behavior of Tests: Heuristic Discussion.- 3 Asymptotic Behavior of Point Estimators: Heuristic Discussion.- 4 Asymptotic Behavior of Confidence Bounds.- 5 Example.- 6 Definitions of Asymptotic Relative Efficiency.- 7 Pitman’s Formula.- 8 Asymptotic Relative Efficiencies of One-Sample Procedures for Shift Families.- 9 Asymptotic Relative Efficiency of Procedures for Matched Pairs.- 10 Asymptotic Relative Efficiency of Two-Sample Procedures for Shift Families.- 11 Asymptotic Efficiency of Kolmogorov-Smirnov Procedures.- Problems.- Tables.- Table A Cumulative Standard Normal Distribution.- Table B Cumulative Binomial Distribution.- Table C Binomial Confidence Limits.- Table D Cumulative Probabilities for Wilcoxon Signed-Rank Statistic.- Table E Cumulative Probabilities for Hypergeometric Distribution.- Table F Cumulative Probabilities for Wilcoxon Rank Sum Statistic.- Table G Kolmogorov-Smirnov Two-Sample Statistic.