Theory Of Rank Tests Research Articles

Robust Nonparametric Methods

(2000). Robust Nonparametric Methods. Journal of the American Statistical Association: Vol. 95, No. 452, pp. 1308-1312.

Theory of Rank Tests

Theory of Rank Tests

An example of a two-sided Wilcoxon signed rank test which is not unbiased

Although the theory of rank tests is rather complete in the one-sided case, it was not even known in 1959, whether the Wilcoxon two-sample test and other similar tests are unbiased against the two-sided alternatives (Lehmann (1959,Testing Statistical Hypotheses, p. 240, Wiley, New York)). A partial answer to this question was given by Sugiura in 1965, who found, that the test named above may be biased (Sugiura (1965,Ann. Inst. Statist. Math.,17, 261–263)). According to Lehmann (1986,Testing Statistical Hypotheses, 2nd ed., pp. 322–324, Wiley, New York) it seems to be still open, whether the same is true for the WILCOXON one-sample test, which is also known as WILCOXON signed rank test. This will be shown in the present paper.

Symmetrized approximate score rank tests for the two-sample case

Rank test statistics for the two-sample problem are based on the sum of the rank scores from either sample. However, a critical difference can occur when approximate scores are used since the sum of the rank scores from sample 1 is not equal to minus the sum of the rank scores from sample 2. By centering and scaling as described in Hajek and Sidak (1967, Theory of Rank Tests, Academic Press, New York) for the uncensored data case the statistics computed from each sample become identical. However such symmetrized approximate scores rank statistics have not been proposed in the censored data case. We propose a statistic that treats the two approximate scores rank statistics in a symmetric manner. Under equal censoring distributions the symmetric rank tests are efficient when the score function corresponds to the underlying model distribution. For unequal censoring distributions we derive a useable expression for the asymptotic variance of our symmetric rank statistics.

The asymptotic efficiency of the kruskal-wallis test and the median test in contingency tables with ordered categories

In a contingency table one classification often corresponds to samples from different populations and the other classification to ordered categories. Methods for analyzing data of this type may be compared using recent extensions in the theory of rank tests by Conover (1973) and Vorlickova (1970) to non-continuous distributions. In this paper the Kruskal-Wallis Test and the Median Test are compared in those situations where the data are given in a contingency table with ordered categoriesf and where one test or the other is optimal. Some comparisons with the Pearson chi-square statistic are given.

Certain Chi-Square Type Tests for Continuous Distributions

Certain Chi-Square Type Tests for Continuous Distributions

BOOK REVIEWS

Book reviewed in this article: Hájek, J., and Sidák, Z. Theory of Rank Tests. Dynkin, E. B., and Yushkevich, A. A. Theorems and Problems on Markov Processes (Russian). Chover, J. (Ed.). Markov Processes and Potential Theory. Proceedings of an Advanced Symposium conducted by the Mathematics Research Center, United States Army, at the University of Wisconsin, Madison, May 1–3, 1967. Murthy, M. N. Sampling Methods and Theory. Sudman, S. Reducing the Cost of Surveys.

The Theory of Rank Tests.

The Theory of Rank Tests.

Theory of Rank Tests.

Theory of Rank Tests.