Grant: Discovery Grants Program - Individual

Although my research program touches on a number of different aspects of statistics and probability theory, my work revolves around a single theme: asymptotics (expansion of a statistic or of a distribution). My research deals with the following main themes: 1. Rectification (further asymptotic expansion) of formulae of coverage probabilities by confidence sets centered at James-Stein and positive-part James-Stein shrinkage estimates. 2. Construction of statistical models for a two-sided crack development for a two-sided cyclic loading of a metallic plate (models of a two-sided Birnbaum-Saunders distribution). Solution of statistical problems of parameter estimation and hypothesis testing for these new models. 3. Consistency problems of some nonclassical bootstrap procedures, especially the asymptotic probability for the deviations of dependent bootstrap means from the sample mean. 4. Guaranteed statistical inference for various schemes of asymptotic analysis. For the problem of statistical quality control, values of the parameter under control should be always considered as a realization of a random variable. The traditional procedures of the control (that ignore this information), usually do not guarantee that a small proportion of defective products are delivered to the consumer, nor that a small proportion of good products get rejected. We can suggest the following, more reliable procedure of guaranteed quality control that guarantee the given constraints on the proportion of defective production delivered to a consumer, and on the proportion of good production that was rejected at the control. The stopping time of the control is achieved if either the posterior probability of the event that the product is defective is less than the given constraint, or the posterior probability of the event that the product is good becomes smaller than another given constraint. The problem is to investigate the asymptotic behavior of the necessary sample size in the framework of this approach to guarantee statistical inference.