Combined Rank Tests for Randomly Censored Paired Data

Abstract

Many authors have dealt with the problem of extending ordinary two-sample rank tests to cases where censoring occurs. Albers and Akritas (1987) proposed simple tests for this purpose, based on the idea of making separate rankings for uncensored and censored observations and subsequently combining the resulting two rank statistics. Similarly, some papers appeared that studied the problem of censoring for the paired-data case rather than the two-sample case. This article indicates how the approach of Albers and Akritas can be adapted to the paired-data case. The tests involved are not based on the ranks of the differences, but the differences of the ranks in the pooled sample. In this way, use is made of interblock information. The asymptotic distribution of the new statistic is obtained under the null hypothesis and contiguous location alternatives. By way of example, Wilcoxon- and Savage-type scores are introduced that are optimal for logistic location and exponential scale alternatives, respectively. The two corresponding tests are applied to some real data, and comparisons are made with the results obtained with competing tests on the same data set.

Key Words:

• Asymptotic efficiency
• Contiguous alternatives
• Hypothesis of symmetry