TABLE of CONTENTS
1 ORDER STATISTICS AND QUANTILES
1.1 Introduction
1.2 Notation
1.3 Distributions of a Single Order Statistic
1.4 Joint Distribution of Two or More Order Statistics
1.5 Distribution of the Range
1.6 Conditional Distribution of Order Statistic
1.7 Expected values and Moments of Order Statistics
1.8 More on Moments
1.9 Practice Problems
2 DISTRIBUTION-FREE STATISTIC
2.1 Distribution-Free Statistic over a \(\mathscr {Z}\)
2.2 Why Rank Statistics Are Distribution-Free
2.3 Counting Statistics
2.4 Ranking Statistics
2.5 Statistics Utilising Counting and Ranking
2.6 Practice Problems
3 U-STATISTICS
3.1 One-Sample U-Statistics
3.2 Some Convergence Results
3.3 The Projection Principle and One Sample \(U\)-Statistics Theorem
3.4 Two-Sample \(U\)-Statistics
4 ASYMPTOTIC RELATIVE EFFICIENCY
4.1 Comparing Two Tests
4.2 Efficacy
4.3 The Efficacy of Rank Tests
4.4 The Efficiency of the Wilcoxon Test
4.5 The Hodges–Lehmann Bound
4.6 Optimal Rank Tests
4.7 Practice Problems