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.

U BANDYOPADHYAY

A MUKHERJEE

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

&nbsp;

The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

&nbsp;

It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Nonparametric Partial Sequential Test for Location Shift at an Unknown Time Point

Sequential Analysis

We introduce a class of nonparametric two-sample tests based on a new partially sequential sampling scheme. Existing partially sequential procedures based on inverse sampling schemes, pioneered by Wolfe (1977) and Orban and Wolfe (1980), are updated in the light of random sequential sampling techniques, proposed by Mukhopadhyay and de Silva (2008). In a quality control setup, the present procedure can be looked upon as a Phase II on-line monitoring with rational subgroups of variable sizes where standards are unknown. We consider a training sample of prefixed size m as Phase I observations and adopt a random sequential sampling in Phase II. We discuss statistical methodologies in detail and provide some asymptotic results. Numerical results based on Monte Carlo are presented to justify asymptotic theory. We computationally investigate the power performances of the proposed test against some fixed alternative. We illustrate our procedure with real data related to water samples for monitoring arsenic contamination. Some concluding remarks along with possible future research problems are offered © 2016, Copyright © Taylor & Francis Group, LLC.

Nonparametric partially random sequential test under Phase II sampling: An illustration to monitor water samples for arsenic contamination

We introduce a class of nonparametric two-sample tests based on a new partially;sequential sampling scheme. Existing partially sequential procedures based on inverse sampling schemes, pioneered by Wolfe (1977) and Orban and Wolfe (1980), are updated in the light of random sequential sampling techniques, proposed by Mukhopadhyay and de Silva (2008), In a quality control setup, the present procedure can be looked upon as a Phase II on-line monitoring with rational subgroups of variable sizes where standards are unknown. We consider a training sample of prefixed size m as Phase I observations and adopt a random sequential sampling in phase II. We discuss statistical methodologies, in detail and provide some asymptotic results. Numerical results based on Monte Carlo are presented to justify asymptotic theory. We cornputationally investigate the power performances of the proposed test against some fixed alternative. We illustrate our procedure with real data related to water samples for monitoring arsenic contamination. Some concluding remarks along with possible future research problems are offered.

SEQUENTIAL ANALYSIS-DESIGN METHODS AND APPLICATIONS

In the present study, we develop two nonparametric partially sequential tests for detecting possible presence of linear trend among the incoming series of observations. We assume that a sample of fixed size is available a priori from some unknown univariate continuous population and there is no sign of trend among these historical observations. Our proposed tests can be viewed as the sequential type tests for monitoring structural changes. We use partial sequential sampling schemes based on usual ranks as well as on sequential ranks. We provide detailed discussion on asymptotic studies related to the proposed tests. We compare the two tests under various situations. We also present some numerical results based on simulation studies. Proposed tests are extremely important in profit making in volatile market through Margin Trading. We illustrate the mechanism with a detailed analysis of a stock price data. © 2011 Elsevier B.V.

Journal of Statistical Planning and Inference

Some partially sequential nonparametric tests for detecting linear trend

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.

Communications in Statistics: Simulation and Computation

Controlling type-I error rate in monitoring structural changes using partially sequential procedures

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. © 2008 Elsevier B.V. All rights reserved.

Journal	Sequential Analysis
Publisher	-
ISSN	0747-4946