Mathematical Sciences: Self-Normalization and Empirical CLT's

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The principal investigator will conduct research on three problems connected with the theory of asymptotic distributions of sums of independent, identically distributed random variables. The first problem is to completely determine the asymptotic distribution of the studentized version of an intermediate, magnitude-trimmed sum for symmetric distributions. The second problem is to empirically reconstruct the distribution of a sum of intermediate length. An affine reconstruction is proposed, via center, scale, and an approximation to the affine-normalized law. The third problem is to investigate a location-invariant approach to magnitude-censoring for sums, utilizing a new centering and scaling technique developed by the principal investigator. The principal investigator will conduct research on three problems connected with the theory of asymptotic distributions of sums of independent, identically distributed random variables. This area of research, limit theory, is at the core of much of classical probability. Problems in this area have been motivated by statistics.