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.

Keywords:

• Arsenic contamination
• Drinking water quality
• Expected sample size
• Geological survey
• Groundwater supply
• Partial sequential sampling
• Patterned alternative
• Wilcoxon score
• World Health Organization

Subject Classifications:

• 62G10
• 62L05

ACKNOWLEDGMENTS

The authors are thankful to the referee, the Associate Editor, and the Editor for their helpful suggestions and dynamic comments. The second author is also grateful to the Council of Scientific and Industrial Research, India, for providing necessary financial support under CSIR sanction F.No.9/28 (594)/2003-EMR-I. The third author is grateful to the deputy director general, Eastern Region, GSI, for providing infrastructural facilities to carry out this research and use these data for the present work.

Notes

Recommended by N. Mukhopadhyay