### 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 language | English (US) |
---|---|

Pages (from-to) | 745-753 |

Number of pages | 9 |

Journal | Annals of the Institute of Statistical Mathematics |

Volume | 44 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 1992 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability

### Cite this

*Annals of the Institute of Statistical Mathematics*,

*44*(4), 745-753. https://doi.org/10.1007/BF00053403

}

*Annals of the Institute of Statistical Mathematics*, vol. 44, no. 4, pp. 745-753. https://doi.org/10.1007/BF00053403

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Symmetrized approximate score rank tests for the two-sample case

AU - Akritas, Michael G.

AU - Johnson, Richard A.

PY - 1992/12/1

Y1 - 1992/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34249839512&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249839512&partnerID=8YFLogxK

U2 - 10.1007/BF00053403

DO - 10.1007/BF00053403

M3 - Article

AN - SCOPUS:34249839512

VL - 44

SP - 745

EP - 753

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 4

ER -