Theory of Rank Tests

Front Cover
Elsevier, Apr 6, 1999 - Mathematics - 435 pages
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.
  • Asymptotic Methods
  • Nonparametrics
  • Convergence of Probability Measures
  • Statistical Inference
 

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Contents

Chapter 1 Introduction and coverage
1
Chapter 2 Preliminaries
10
Chapter 3 Elementary theory of rank tests
35
Chapter 4 Selected rank tests
94
Chapter 5 Computation of null exact distributions
165
Chapter 6 Limiting null distributions
183
Chapter 7 Limiting nonnull distributions
249
Chapter 8 Asymptotic optimality and efficiency
299
Chapter 9 Rank estimates and asymptotic linearity
358
Chapter 10 Miscellaneous topics in regression rank tests
383
Bibliography
407
Subject index
425
Author index
429
Index of mathematical symbols
433
Titles in this series
437
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About the author (1999)

Zbynek Šidák was Chairman, Department of Probability and Statistics at the Mathematical Institute, Academy of Sciences, Czech Republic. He is now the principal research worker there. He has worked at various American universities as well. For 30 years, he was Editor of the journal Applications of Mathematics. His interests in statistics were rank tests, multivariate and cluster analysis, ranking and selection procedures, and Markov chains.

Pranab K. Sen is Cary C. Boshamer Professor of Biostatistics and Statistics at the University of North Carolina, and is a Fellow of the Institute of Mathematical Statistics and of the American Statistical Association. He is also an elected member of the International Statistical Institute.Prenab K. Sen is author or co-author of multiple volumes in Mathematical Statistics, Probability Theory and Biostatistics, and has published extensively in nonparametrics, multivariate and sequential analysis, and reliability and survival analysis.

Jaroslav Hájek was Professor and Chairman, Department of Probability and Statistics at Charles University, Prague, Czech Republic, and also a Visiting Professor at several American universities. His contributions to statistics are very profound, especially in rank test theory, survey sampling, estimation theory, and statistics in random processes. He died in 1974 at the age of 48.

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