Mathematical Sciences: Adaptive Distribution-free in Design of Experiments

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The purpose of this project is to provide a class of adaptive nonparametric procedures similar to Hogg's procedures, but for more general situations, including (I) testing for ordered alternatives in the c-sample location problem (c2), (ii) testing for ordered alternatives in the c-sample scale problem, (iii) testing in the c-sample location - scale problem, (iv) testing, estimation and multiple comparisons in the one-way layout, two-way layout and multi-way layout analysis of variance (ANOVA) models. In addition, we will resolve the practical problem of handling ties. Based on the theoretical arguments as well as some extensive Monte Carlo studies, the supremacy of the procedures over (I) the usual (non-adaptive) procedure of working only with the ranks and the resulting statistics, such as Wilcoxon, and (ii) the usual parametric procedure (based on the assumption of normality of the underlying distribution function) will be established. This project will broaden the knowledge and explore new techniques related to the study of the adaptive distribution free procedures in several problems in the analysis of variance (univariate as well as multivariate), multiple comparisons, estimation of contrasts, among others. It will enhance the existing techniques and assist the future research projects in the related fields.