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Concepts of Nonparametric Theory

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...

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Bibliographic Details
Main Authors: Pratt, J.W., Gibbons, J.D. (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 1981, 1981
Edition:1st ed. 1981
Series:Springer Series in Statistics
Subjects:
Applications Of Mathematics
Mathematics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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
  • 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
  • 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
  • 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

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