Before pooling data on effect sizes (a generic term for parameters of interest in the context of meta-analysis) from different studies, it is important to test for homogeneity of the effect sizes. A well known test for homogeneity is based on Cochran’s chisquare statistic. Our recent investigation showed that when the effect size of interest is a pairwise correlation, Cochran’s homogeneity test...

1.1 Deciding between two simple hypotheses: the Neyman-Pearson Lemma. Probability theory is reviewed in Appendix D. Suppose an experiment has a set X of possible outcomes. The outcome has some probability distribution µ defined on X. In statistics, we typically don't know what µ is, but we have hypotheses about what it may be. After making observations we'll try to make a decision between or am...

In the modern Big Data analysis, testing multiple hypotheses simultaneously has been an important tool in analyzing data arising from scientific studies, such as genetics, astronomy, social sciences and many others. The hypotheses can often be grouped together according to the nature of the scientific investigations. For instance, genes can be grouped according to gene pathways; the nearby pixe...

The approach of controlling the false discovery rate (FDR) which is less conservative than controlling the family wise error rate (FWER) has become a new and popular multiple testing procedure in microarray studies. In addition to multiple testing problems the limitation of sample size is another big challenge in this area. This thesis addresses the problem of multiple testing in the context of...

We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity against a composite one-sided parametric alternative that this is a self-correcting point process. The underlying family of measures is locally asymptotically quadratic and we describe the behavior of score function, likelihoo...

We study the problem of testing composite hypotheses versus composite alternatives, using a convex duality approach. In contrast to classical results obtained by Krafft & Witting [11], where sufficient optimality conditions are obtained via Lagrange duality, we obtain necessary and sufficient optimality conditions via Fenchel duality under some compactness assumptions. This approach also differ...

In traditional statistics all parameters of the mathematical model and possible observations should be well defined. Sometimes such assumption appears too rigid for the real-life problems, especially while dealing with linguistic data or imprecise requirements. To relax this rigidity fuzzy methods are incorporated into statistics. We review hitherto existing achievements in testing statistical ...