Inverse Sampling Based on General Scores for Non-Parametric Two-Sample Problems

Abstract: In the present work, we introduce a partial sequential sampling scheme to develop a sequential rank-based nonparametric test for the identity of two unknown univariate continuous distribution functions against one-sided shift in location occurring at an unknown time point. Our work is motivated by Wolfe (1977) as well as Orban and Wolfe (1980). We provide detailed discussion on asymptotic studies related to the proposed test. We compare the proposed test with a usual rank-based test. Some simulation studies are also presented.

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.

Abstract: In the present article, we develop some asymptotically power on partially sequential nonparametric tests for monitoring structural changes. Our test procedures are based on Wilcoxon score. We use the idea of curved stopping boundaries. We derive some exact results and perform simulation studies to provide various properties of the tests. We see that one of the proposed procedures significantly controls the Type I error rate. This procedure may be very effective for fluctuation monitoring. We illustrate the procedures by using real life data from the stock market.

Abstract: Financial or economic crisis of 2008 and its severe negative impact on the human race is currently one of the focal themes of financial research. During this crisis period the Indian Rupee (INR) has significantly lost its ground compared to the United States Dollar (USD). In the present paper, we address the issues identifying warning and action points in a time sequential monitoring of the exchange rate records. We developed some approximate power 1 partially sequential nonparametric tests that are based on both usual and sequential ranks. Proposed procedures necessarily help us to capitalize the best features of the two different rank procedures. We use Wilcoxon score and the idea of curved stopping boundaries as in Bandyopadhyay et al. (2008). We vividly present our numerical findings obtained by sequential Monte-Carlo procedures. We aim at controlling the type I error rate in course of structural monitoring.

Abstract: In the present paper we introduce a partially sequential sampling procedure to develop a nonparametric method for simultaneous testing. Our work, as in [U. Bandyopadhyay, A. Mukherjee, B. Purkait, Nonparametric partial sequential tests for patterned alternatives in multi-sample problems, Sequential Analysis 26 (4) (2007) 443–466], is motivated by an interesting investigation related to arsenic contamination in ground water. Here we incorporate the idea of multiple hypotheses testing as in [Y. Benjamini, T. Hochberg, Controlling the false discovery rate: A practical and powerful approach to multiple testing, Journal of Royal Statistical Society B 85 (1995) 289–300] in a typical way. We present some Monte Carlo studies related to the proposed procedure. We observe that the proposed sampling design minimizes the expected sample sizes in different situations. The procedure as a whole effectively describes the testing under dual pattern alternatives. We indicate in brief some large sample situations. We also present detailed analysis of a geological field survey data.

Abstract: A class of test procedures is proposed for the two-sample setting when one of the samples has a fixed sample size, and the second is obtained by an inverse binomial sequential sampling scheme. These procedures allow either a classical approach or a completely nonparametric attack to a wide variety of two-sample problems, Properties of the tests are discussed, Including limiting distributions as the fixed sample size tends to infinity, and the capability of obtaining asymptotic power restrictions against specified alternatives of interest. Criteria for selecting a particular procedure are discussed.

Abstract: Io (3.10) (p 50, first line) of the paper, it was stated that hr.mEv+ in ~ the one-sided case <-win the two-sided case). But as with r tending to ao ,m also tends to infinity, the conditional argument given in support of this was not correct. However, the conclusion (3.10), and hence, Theorem 3.1 holds, This can be seen as follows. It may be verified that {S n .m ; l <;n < r} where S n .m is given by ( 3.4 ), is a martingale sequence uader 8 0 • Applying Theorem 2 of Brown (1971, p 60), it can be easily shown that, under H 0 , for fixed t,