Simultaneous semi-sequential testing of dual alternatives for pattern recognition

In this paper, we propose a new nonparametric simultaneous test for dual alternatives. Simultaneous tests for dual alternatives are used for pattern detection of arsenic contamination level in ground water. We consider two possible patterns, namely, monotone shift and an umbrella-type location alternative, as the dual alternatives. Pattern recognition problems of this nature are addressed in Bandyopadhyay et al. [5], stretching the idea of multiple hypotheses tests as in Benjamini and Hochberg [6]. In the present context, we develop an alternative approach based on contrasts that helps us to detect three underlying pattern much more efficiently. We illustrate the new methodology through a motivating example related to highly sensitive issue of arsenic contamination in ground water. We provide some Monte-Carlo studies related to the proposed technique and give a comparative study between different detection procedures. We also obtain some related asymptotic results.