A Near-Nonparametric Partially Sequential Test for Monitoring Phase II Location Under Pairwise Dependence Between Two Phases

Abstract

In the present work, we introduce a partially sequential test for monitoring the location parameter of a population at phase II when a standard sample of prefixed size from phase I population is available. We consider a typical pairwise dependence between the samples from phase I and phase II. The entire problem is motivated from the statistical issues related to environmental monitoring. The proposed test is primarily based on ranks and hence it is closely nonparametric in nature. We use an inverse sampling scheme for collecting samples in phase II. Asymptotic distribution of the stopping variable is derived under suitable assumptions. We carry out detailed simulation studies to examine the power performance of the proposed test. Some numerical findings obtained through Monte Carlo studies are summarized graphically. The key advantage of the proposed method over traditional fixed-sample-size-based tests is its quicker detection property with high precision. This helps us to save precious phase II samples in various situations. We also provide a simple worked-out example based on acidic precipitation data to illustrate our proposed procedure.

Keywords:

• Acidic precipitation
• Arsenic contamination
• Bivariate population
• Rank
• Semi sequential test
• Test for location

Subject Classifications:

• 62G10
• 62L05

ACKNOWLEDGMENTS

Thanks are due to the former Director of Geological Survey of India, Dr. Barendra Purkait, for introducing the author to the geological problem related to the monsoon effect on arsenic contamination. The author would also like to thank the anonymous referee, the Associate Editor and the Editor for their comments and suggestions. A major part of this work was carried out during the author's stay in the Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden.

Notes

Recommended by Y. I. Chang