Problems on the Asymptotic Behavior of Functionals of the Empirical Distribution

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0203865Mason Problems on the asymptotic behavior of functionals of the empirical distribution have long attracted the interest of probabilists and have led to the development of new methods and theory that have enriched both mathematical statistics and probability theory. A classic example is the problem of the asymptotic distribution of the Kolmogorov-Smirnov statistic, which ultimately led to the development of the theory of weak convergence and strong approximations. Over the next few years the investigator plans to concentrate his efforts on large sample theory problems connected with particular functionals of the empirical distribution. These include the L1-norm density estimator process, integral functionals of density estimators and local empirical and U-statistics processes. The anticipated results should have potential use in the development of a class of practical goodness-of-fit techniques and statistical estimators. In fact, these investigations have already given rise to a number of new methods to assess and describe in an intelligent way the behavior of the underlying mechanism that generates natural phenomena.