Nonparametric Partial Sequential Tests for Patterned Alternatives in Multisample Problems

Abstract

In the present work we develop partial sequential nonparametric tests for multiple comparison. We provide tests for the identity of several unknown univariate continuous distribution functions against patterned alternatives. Our tests are based on Wilcoxon score. We conduct some Monte Carlo studies related to the proposed tests. We carry out a detailed comparison between the proposed procedures and the corresponding nonsequential procedures. We register significant gain in sample size through the proposed procedure, maintaining almost the same level and power for both the tests. We perform an analysis of life data arising out of a geological survey related to arsenic contamination. We also present some asymptotics in this context.

Simultaneous tests for patterned recognition using nonparametric partially sequential procedure

“…, s. We have seen that this value is r even for moderately large m. However, from (3.4), we see that the actual numbers of sample observations considered from the test populations will not increase because an increasing pattern of M i 's means a decreasing pattern of M i 's. Equipped with the above, we now slightly modify Y -statistics introduced by Bandyopadhyay et al [4] for a monotone trend and patterned alternatives and use them simultaneously.…”

“…In the same line of thinking, Bandyopadhyay et al [4] considered a nonparametric test for decreasing trend among the different populations by using the statistic given by:…”

“…Bandyopadhyay et al [4] developed a sequential version of [9] type tests for patterned alternatives. For fixed sample sizes from all the populations, Hettmansperger and Norton [9] developed a test statistic based on R i j , where R i j is the rank of the jth observation of the ith population in the combined data, where j = 1, 2, .…”

“…In the present work we consider such a partial sequential technique for dual patterned alternative. Here we extend several partially sequential sample problems as in [7,4].…”

“…It occurs in typically young areas formed by Quaternary aquifers in alluvial and deltaic sediments. Bandyopadhyay et al [4] presents an elaborate discussion on the presence of arsenic in ground water, impact of arsenic on human health and various recent initiatives by different organizations. For further discussion one may see, for example, [1,11,18,19,14].…”