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.     

Unbalanced and Partial Group Sequential Methods for Normal Responses in Clinical Trials

Abstract

Group sequential methods for a two-treatment clinical trial with normal responses are discussed. First we consider the case where the sample sizes for two treatments are possibly unequal between the treatments due to an unequal randomization. Then we discuss group sequential design in the context of a historical control study, that is, under the partial sequential sampling scheme, in which the samples on one treatment, say control, are available at the outset, and the samples on the other treatment, say experimental, are obtained in the group sequential way. We discuss the cases of known and unknown variance for both unbalanced and partial group sequential setups. All of the procedures are discussed with numerical studies.     

Sequential slippage tests using Robbins-Lai's invariant confidence sequences

The paper deals with two kinds of location-slippage testing problems.The alternative hypothesis says that there is a single slippage in one kind of problems,and that there are multiple slippages in the other kind. In a location slippage model, by using Robbins' inequality, Robbins-Lai's invariant confidence sequences for slippage are constructed for both of the problems and sequential slippage tests using those confidence sequences are proposed.     

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

Abstract

A sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples. Unbiased estimators are applied to infer the parameters of multidimensional or multinomial random walks that are observed until they reach a boundary. Clinical trials are shown to be representable within this scheme and an application to the estimation of the multinomial probabilities following multinomial clinical trials is presented.     

Sequential procedures for monltoring the parameters of the autoregressive model relative to unspecified targets

Sequential procedures are developed for monitoring the parameters of a time dependent autoregressive model relative to unspecified targets. Such a problem arises when we need to monitor the parameters for changes from their unknown initial values (the unspecified targets), instead of from specified targets. For this purpose, scores type statistics are proposed which: (1) reflect changes in the parameters from their initial values without requiring any input about these values; and (2) are aimed at detecting arbitrary shifts in the parameters, instead of at restrictive "one point" shift alternatives. The procedures developed are capable of monitoring any one of, or any combination of, the mean, variance or correlation structure of an autoregressive sequence of known finite order. Their false signal rates are controlled, and their performance under local shift     

On sequentially adaptive asymptotically efficient rank statistics

For the simple regression model ( containing the two—sample location model as a special case ), adaptive ( linear ) rank statistics arising in the context of ( asymtotically) efficient testing and estimation procedures are considered. An orthonormal system based on the classical Legendre polynomial system is incorporated in the adaptive determination of the score generating function, and the proposed sequential procedure is based on a suitably posed stopping rule. Various properties of this sequentailly adaptive procedure and the allied stopping rule are studied. Asymptotic linearity results ( in a shift or regression parameter ) of linear rank statistics are studied with special reference to the Legendre polynomial system and some improved rates of convergence are estabilished in this context.