Theory of Rank Tests
Regular price
17.500 KD
inc. VAT
Couldn't load pickup availability
Table of contents
- Cover
- Contentsix
- Preface to the Second Editionv
- Preface to the First Editionvii
- Chapter 1. Introduction and coverage1
- 1.1 THE BACKGROUND1
- 1.2 ORGANIZATION OF THE PRESENT TREATISE5
- Chapter 2. Preliminaries10
- 2.1 BASIC NOTATION10
- 2.2 FAMILIES OF ONE-DIMENSIONAL DENSITIES13
- 2.3 TESTING HYPOTHESES22
- 2.4 AUXILIARY RESULTS FOR NORMAL SAMPLES29
- Problems and complements to Chapter231
- Chapter 3. Elementary theory of rank tests35
- 3.1 RANKS AND ORDER STATISTICS35
- 3.2 PERMUTATION, tNVARIANT, AND RANK TESTS41
- 3.3 EXPECTATIONS AND VARIANCES OF LINEAR RANK STATISTICS57
- 3.4 LOCALLY MOST POWERFUL RANK TESTS64
- 3.5 STATISTICAL FUNCTIONALS79
- Problems and complements to Chapter 385
- Chapter 4. Selected rank tests94
- 4.1 TWO-SAMPLE TESTS OF LOCATION95
- 4.2 TWO-SAMPLE TESTS OF SCALE103
- 4.3 REGRESSION108
- 4.4 THREE OR MORE SAMPLES112
- 4.5 TESTS OF SYMMETRY117
- 4.6 TESTS OF INDEPENDENCE121
- 4.7 RANDOM BLOCKS128
- 4.8 TREATMENT OF TIES130
- 4.9 RANK TESTS FOR CENSORED DATA136
- 4.10 MULTIVARIATE RANK TESTS152
- Problems and complements to Chapter 4160
- Chapter 5. Computation of null exact distributions165
- 5.1 DIRECT USE OF DISTRIBUTION OF RANKS165
- 5.2 EXPLICIT FORMULAS FOR DISTRIBUTIONS168
- 5.3 RECURRENCE FORMULAS FOR DISTRIBUTIONS173
- 5.4 IMPROVEMENTS OF LIMITING DISTRIBUTIONS177
- Problems and complements to Chapter 5179
- Chapter 6. Limiting null distributions183
- 6.1 SIMPLE LINEAR RANK ST4TISTICS183
- 6.2 RANK STATISTICS OF x2-TYPES203
- 6.3 STATISTICS OF KOLMOGOROV-SMIRNOV TYPES209
- 6.4 FUNCTIONAL CENTRAL LIMIT THEOREMS230
- Problems and complements to Chapter 6240
- Chapter 7. Limiting non-null distributions249
- 7.1 CONTIGUITY249
- 7.2 SIMPLE LINEAR RANK STATISTICS262
- 7.3 FAMILIES OF SIMPLE LINEAR RANK STATISTICS276
- 7.4 ASYMPTOTIC POWER,281
- 7.5 NON-CONTIGUOUS ALTERNATIVES289
- Problems and complements to Chapter 7294
- Chapter 8. Asymptotic optimality and efficiency299
- 8.1 ASYMPTOTICALLY OPTIMUM TESTS299
- 8.2 ASYMPTOTIC EFFICIENCY OF TESTS316
- 8.3 BAHADUR EFFICIENCY325
- 8.4 HODGES-LEHMANN DEFICIENCY336
- 8.5 ADAPTIVE RANK TESTS341
- Problems and complements to Chapter 8352
- Chapter 9. Rank estimates and asymptotic linearity358
- 9.1 R-ESTIMATES OF LOCATION AND REGRESSION358
- 9.2 ASYMPTOTIC LINEARITY OF RANK STATISTICS IN REGRESSION PARAMETERS366
- 9.3 RANK ESTIMATION OF REGRESSION PARAMETERS378
- Problems and complements to Chapter 9382
- Chapter 10. Miscellaneous topics in regression rank tests383
- 10.1 ALIGNED RANK TESTS383
- 10.2 REGRESSION RANK SCORES394
- 10.3 RANK VERSUS OTHER ROBUST PROCEDURES399
- Problems and complements to Chapter 10 . .404
- Bibliography407
- Subject index425
- Author index429
- Index of mathematical symbols433
- Titles in this series437
The first edition of Theory of Rank Tests (1967) has been the precursor to a unified and theoretically motivated treatise of the basic theory of tests based on ranks of the sample observations. For more than 25 years, it helped raise a generation of statisticians in cultivating their theoretical research in this fertile area, as well as in using these tools in their application oriented research. The present edition not only aims to revive this classical text by updating the findings but also by incorporating several other important areas which were either not properly developed before 1965 or have gone through an evolutionary development during the past 30 years. This edition therefore aims to fulfill the needs of academic as well as professional statisticians who want to pursue nonparametrics in their academic projects, consultation, and applied research works.
Key Features
* Asymptotic Methods
* Nonparametrics
* Convergence of Probability Measures
* Statistical Inference
Key Features
* Asymptotic Methods
* Nonparametrics
* Convergence of Probability Measures
* Statistical Inference