John Orban

Abstract: The concept of a partially sequential hypothesis test was introduced by Wolfe (1977a), an{associated procedures were developed for both parametric and nonparametric assumptions In this paper we consider distribution-free extensions of those indicator tests, based on the placements of the sequentially obtained observations among the previously collected fixed size sample Exact and asymptotic, as the fixed sample size in¬creases to infinity, properties of these sequential placements procedures are obtained, including statements about the power and expected number of sequentially obtained observations The results of a Monte Carlo study are used to differentiate be¬tween various placement scoring schemes

Abstract: SUMMARY Wolfe (1977a) introduced the concept of a partially sequential two-sample hypothesis test and studied some of the properties for a general class of such procedures. In this paper we deal with criteria for selecting an indicator set for use in a partially sequential test. In particular, we show how the Neyman-Pearson lemma can be used to generate an asymptotically optimal indicator set, in the sense that it corresponds to an asymptotically most powerful partially sequential test. In addition, we provide an accurate upper bound for the asymptotic expected sample size of the sequentially obtained observations, and obtain a closed form approximation for the maximum number of these observations necessary in order to obtain prespecified asymptotic power bounds against alternatives of interest. Some key word8: Asymptotically most powerful partially sequential test; Asymptotic power bound; Expected sample size; Negative binomial distribution; Optimal indicator set; Partially sequential procedure; Two-sample test.

Abstract: We consider a class of two-sample distribution-free tests that are appropriate for situations where one of the sample sizes is large relative to the other. These procedures are based on the placements of the observations in the smaller sample among the ordered observations in the larger sample, and this class of tests generalizes the Mann-Whitney (1947) procedure in much the same way that the class of linear rank tests generalizes the equivalent Wilcoxon (1945) rank sum form. Optimality criteria for choosing a test from this class are discussed and limiting distributions for the associated class of test statistics are determined for the case where only one of the sample sizes goes to infinity.

Abstract: In this paper we propose a class of distribution-free tests for the treatments versus control setting using the partially sequential sampling technique. Expressions for the asymptotic distributions and power for the tests are provided and criteria for adapting a particular test to have asymptotic power restrictions against alternatives of interest are discussed. Comparative results of a Monte Carlo power study are also presented.

Abstract: An overview of some nonparametric procedures based on precedence (or exceedance) statistics is given. The procedures include both tests and confidence intervals. In particular, the construction of some simple distribution-free confidence bounds for location difference of two distributions with the same shape is considered and some properties are derived. The asymptotic relative efficiency of an asymptotic form of the corresponding test relative to Wilcoxon's two-sample rank sum test and the two-sample Student t-test is given for various cases. Some K-sample problems are discussed where precedence-type tests are useful, along with a review of the literature.

Abstract: The concept of a partially sequential hypothesis test was introduced by Wolfe (1977a), an{associated procedures were developed for both parametric and nonparametric assumptions In this paper we consider distribution-free extensions of those indicator tests, based on the placements of the sequentially obtained observations among the previously collected fixed size sample Exact and asymptotic, as the fixed sample size in¬creases to infinity, properties of these sequential placements procedures are obtained, including statements about the power and expected number of sequentially obtained observations The results of a Monte Carlo study are used to differentiate be¬tween various placement scoring schemes

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.