Author | Pratt, John W. author |
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Title | Concepts of Nonparametric Theory [electronic resource] / by John W. Pratt, Jean D. Gibbons |
Imprint | New York, NY : Springer New York, 1981 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5931-2 |
Descript | 462 p. online resource |
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 the Y โ 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 Pitmanโs 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