ON LARGE DEVIATIONS OF LINEAR RANK STATISTICS.
STANFORD UNIV CALIF DEPT OF STATISTICS
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Linear rank statistics are studied. This group of statistics includes many of those used in nonparametric procedures. The main theorem gives an asymptotic expression for the probability of a large deviation of such a statistic. This theorem is applied to the two sample problem, and also the problem of testing bivariate independence where it is used to obtain asymptotic as alpha approaches zero, beta fixed expressions for the sample sizes needed by nonparametric tests to achieve type I error alpha and type II error beta against a fixed, simple alternative. It is shown that the Fisher-Yates correlation coefficient requires exactly the same asymptotic sample size against a bivariate normal alternative as the product-moment correlation coefficient. Author
- Statistics and Probability