Mathematical Sciences: Quantile-Uniform Empirical Distribution Function Methods in Probability Theory

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The principal investigator will continue to exploit the representation of a sequence of independent identically distributed random variables as the sequence of the quantile function observed at independent identically distributed uniform variables. The quantile function is the left continuous inverse of the distribution function. This representation provides a strong connection between the partial sums of random variables and the empirical process. The principal investigator, along with a number of collaborators, has used this technique over last several years to get many interesting results. Specific problems of study include the Kiefer process version of the weighted approximations, convergence of Bahadur-Kiefer type process, convergence of weighted sums of order statistics, and iterated logarithm laws for the sums of extreme values.