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Produktbild: Concepts of Nonparametric Theory
- 11%

Concepts of Nonparametric Theory

Aus der Reihe Springer Series in Statistics
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77,99 € UVP 88,00 €

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

01.12.1981

Verlag

Springer New York

Seitenzahl

462

Maße (L/B/H)

1/1/1 cm

Gewicht

835 g

Auflage

1981.

Sprache

Englisch

ISBN

978-0-387-90582-2

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

01.12.1981

Verlag

Springer New York

Seitenzahl

462

Maße (L/B/H)

1/1/1 cm

Gewicht

835 g

Auflage

1981.

Sprache

Englisch

ISBN

978-0-387-90582-2

Herstelleradresse

Springer Heidelberg
Tiergartenstr. 17
69121 Heidelberg
DE
buchhandel-buch@springer.com

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  • Produktbild: Concepts of Nonparametric Theory
  • 1 Concepts of Statistical Inference and the Binomial Distribution.- 1 Introduction.- 2 Probability Distributions.- 3 Estimators and their Properties.- 3.1 Unbiasedness and Variance.- 3.2 Consistency.- 3.3 Sufficiency.- 3.4 Minimum Variance.- 4 Hypothesis Testing.- 4.1 Tests and their Interpretation.- 4.2 Errors.- 4.3 One-Tailed Binomial Tests.- P-values.- 4.5 Two-Tailed Test Procedures and P-values.- 4.6 Other Conclusions in Two-Tailed Tests.- 5 Randomized Test Procedures.- 5.1 Introduction: Motivation and Examples.- 5.2 Randomized Tests: Definitions.- 5.3 Nonrandomized Tests Equivalent to Randomized Tests.- 5.4 Usefulness of Randomized Tests in Theory and Practice.- 5.5 ?Randomized P-values.- 6 Confidence Regions.- 6.1 Definition and Construction in the Binomial Case.- 6.2 Definition of Confidence Regions and Relationship to Tests in the General Case.- 6.3 Interpretation of Confidence Regions.- 6.4 True Confidence Level.- 6.5 Including False Values and the Size of Confidence Regions.- 6.6 ?Randomized Confidence Regions.- 7 Properties of One-Tailed Procedures.- 7.1 Uniformly Most Powerful One-Tailed Tests.- 7.2 ?Admissibility and Completeness of One-Tailed Tests.- 7.3 Confidence Procedures.- 7.4 ?Proofs.- 8 Choice of Two-Tailed Procedures and their Properties.- 8.1 Test Procedures.- 8.2 Confidence Procedures.- 8.3 ?Completeness and Admissibility of Two-Conclusion Two-Tailed Tests.- 8.4 ?Completeness and Admissibility of Three-Conclusion Two-Tailed Tests.- 9 Appendices to Chapter 1.- A Limits of the Binomial Distribution.- A.1 Ordinary Poisson Approximation and Limit.- A.2 Ordinary Normal Approximation and Limit.- ? Convergence in Distribution and Asymptotic Distributions.- B.1 Convergence of Frequency Functions and Densities.- B.2 Convergence in Distribution.- B.3 Two Central Limit Theorems.- 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.- 3.1 Test Procedures.- 3.2 “Optimum” Properties.- 3.3 ?Proofs.- 4 Confidence Procedures Based on the Sign Test.- 5 Interpolation between Attainable Levels.- 6 The Sign Test with Zero Differences.- 6.1 Discussion of Procedures.- 6.2 Conditional Properties of Conditional Sign Tests.- 6.3 Unconditional Properties of Conditional Sign Tests.- 6.4 ?Proof for One-Sided Alternatives.- 6.5 ?Prooffor Two-Sided Alternatives.- 7 Paired Observations.- 8 Comparing Proportions using Paired Observations.- 8.1 Test Procedure.- 8.2 Alternative Presentations.- 8.3 Example.- 8.4 Interpretation of the Test Results.- 8.5 Properties of the Test.- 8.6 Other Inferences.- 8.7 Cox Model.- 9 Tolerance Regions.- 9.1 Definition.- 9.2 Practical Uses.- 9.3 Construction of Tolerance Regions: Wilks’ Method.- 9.4 Tolerance Regions for Description.- 9.5 Tolerance Regions for Prediction.- 9.6 More General Construction Procedures.- 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.- 3.1 Test Procedure and Exact Null Distribution Theory.- 3.2 Asymptotic Null Distribution Theory.- 3.3 Large Sample Power.- 3.4 Consistency.- 3.5 Weakening the Assumptions.- 4 Confidence Procedures Based on the Wilcoxon Signed-Rank Test.- 5 A Modified Wilcoxon Procedure.- 6 Zeros and Ties.- 6.1 Introduction.- 6.2 Obtaining the Signed Ranks.- 6.3 Test Procedures.- 6.4 Warnings and Anomalies: Examples.- 6.5 Comparison of Procedures.- 7 Other Signed-Rank Procedures.- 7.1 Sums of Signed Constants.- 7.2 Signed Ranks and Walsh Averages.- 7.3 Confidence Bounds Corresponding to Signed-Rank Tests.- 7.4 Procedures Involving a Small Number of Walsh Averages.- 8 Invariance and Signed-Rank Procedures.- 8.1 Permutation Invariance.- 8.2 Invariance under Increasing, Odd Transformations.- 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.- 2.1 Tests.- 2.2 Weakening the Assumptions.- 2.3 Related Confidence Procedures.- 2.4 Properties of the Exact Randomization Distribution.- 2.5 Modifications and Approximations to the Exact Randomization Procedure.- 3 The General Class of One-Sample Randomization Tests.- 3.1 Definition.- 3.2 Properties.- 4 Most Powerful Randomization Tests.- 4.1 General Case.- 4.2 One-Sided Normal Alternatives.- 4.3 Two-Sided Normal Alternatives.- 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.- 3.1 Reduction of Data to a 2 × 2 Table.- 3.2 Fisher’s Exact Test for 2 × 2 Tables.- 3.3 Ties.- 3.4 Corresponding Confidence Procedures.- 3.5 Power.- 3.6 Consistency.- 3.7 “Optimum” Properties.- 3.8 Weakening the Assumptions.- 4 Procedures Based on Sums of Ranks.- 4.1 The Rank Sum Test Procedure.- 4.2 Null Distribution of the Rank Sum Statistics.- 4.3 Corresponding Confidence Procedures.- 4.4 Approximate Power.- 4.5 Consistency.- 4.6 Weakening the Assumptions.- 4.7 Ties.- 4.8 Point and Confidence Interval Estimation of P(X > Y).- 5 Procedures Based on Sums of Scores.- 6 Two-Sample Rank Tests and the Y — X Differences.- 7 Invariance and Two-Sample Rank Procedures.- 8 Locally Most Powerful Rank Tests.- 8.1 Most Powerful and Locally Most Powerful Rank Tests Against Given Alternatives.- 8.2 The Class of 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.- 2.1 Tests.- 2.2 Weakening the Assumptions.- 2.3 Related Confidence Procedures.- 2.4 Properties of the Exact Randomization Distribution.- 2.5 Approximations to the Exact Randomization Distribution.- 3 The Class of Two-Sample Randomization Tests.- 3.1 Definition.- 3.2 Properties.- 4 Most Powerful Randomization Tests.- 4.1 General Case.- 4.2 One-Sided Normal Alternatives.- 4.3 Two-Sided Normal Alternatives.- Problems.- 7 Kolmogorov-Smirnov Two-Sample Tests.- 1 Introduction.- 2 Empirical Distribution Function.- 3 Two-Sample Kolmogorov-Smirnov Statistics.- 4 Null Distribution Theory.- 4.1 An Algorithm for the Exact Null Distribution.- 4.2 Relation Between One-Tailed and Two-Tailed Procedures.- 4.3 Exact Formulas for Equal Sample Sizes.- 4.4 Asymptotic Null Distributions.- 5 Ties.- 6 Performance.- 7 One-Sample Kolmogorov-Smirnov Statistics.- Problems.- 8 Asymptotic Relative Efficiency.- 1 Introduction.- 2 Asymptotic Behavior of Tests: Heuristic Discussion.- 2.1 Asymptotic Power of a Test.- 2.2 Nuisance Parameters.- 2.3 Asymptotic Relative Efficiency of Two Tests.- 3 Asymptotic Behavior of Point Estimators: Heuristic Discussion.- 3.1 Estimators of the Same Quantity.- 3.2 Relation of Estimators and Tests.- 3.3 Estimators of Different Quantities.- 4 Asymptotic Behavior of Confidence Bounds.- 5 Example.- 6 Definitions of Asymptotic Relative Efficiency.- 6.1 Introduction.- 6.2 Tests.- 6.3 Estimators.- 6.4 Confidence Bounds.- 6.5 Confidence Intervals.- 6.6 Summary.- 7 Pitman’s Formula.- 8 Asymptotic Relative Efficiencies of One-Sample Procedures for Shift Families.- 8.1 The Shift Model.- 8.2 Asymptotic Relative Efficiencies for Specific Shift Families.- 8.3 Bounds on Asymptotic Relative Efficiencies for Shift Families.- 8.4 ?Asymptotically Efficient Signed-Rank Procedures.- 9 Asymptotic Relative Efficiency of Procedures for Matched Pairs.- 9.1 Assumptions.- 9.2 Bounds for Asymptotic Efficiencies for Matched Pairs.- 10 Asymptotic Relative Efficiency of Two-Sample Procedures for Shift Families.- 11 Asymptotic Efficiency of Kolmogorov-Smirnov Procedures.- 11.1 One-Sided Tests.- 11.2 Two-Sided Tests.- 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.