Symmetrized approximate score rank tests for the two-sample case

Michael G. Akritas, Richard A. Johnson

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)745-753
Number of pages9
JournalAnnals of the Institute of Statistical Mathematics
Volume44
Issue number4
DOIs
StatePublished - Dec 1 1992

Fingerprint

Rank Test
Score Test
Rank Statistics
Censoring
Two-sample Problem
Score Function
Asymptotic Variance
Censored Data
Unequal
Test Statistic
Statistic
Scaling
Statistics

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

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abstract = "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.",
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Symmetrized approximate score rank tests for the two-sample case. / Akritas, Michael G.; Johnson, Richard A.

In: Annals of the Institute of Statistical Mathematics, Vol. 44, No. 4, 01.12.1992, p. 745-753.

Research output: Contribution to journalArticle

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