Theory of Rank Tests
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.
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Chapter 4 Selected rank tests
Chapter 5 Computation of null exact distributions
Chapter 6 Limiting null distributions
Chapter 7 Limiting nonnull distributions
Chapter 8 Asymptotic optimality and efficiency
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absolutely continuous aligned rank tests alternatives approximate arbitrary assume asymp asymptotic efficiency asymptotic linearity asymptotic power asymptotically normal asymptotically optimum basic Brownian bridge censoring scheme Chapter coefficient conditional consider convergence converges in distribution corresponding critical region defined denote density f distribution function empirical distribution function equals equivalent estimates finite Fisher information formula function F g-field given Hájek hence holds implies independent invariance Jurecková Kolmogorov–Smirnov Lemma linear models linear rank statistics locally most powerful martingale median test multivariate non-central non-decreasing normal distribution Note null hypothesis observations order statistics permutation permutation tests powerful rank test powerful test properties R-estimates random variables respectively satisfy score function Section sequence stochastic Subsection symmetric test based test statistic theory of rank tion two-sample variance vector Wilcoxon test