Problems on the Asymptotic Behavior of Functionals of the Empirical Distribution

0203865梅森问题的渐近行为的泛函的经验分布长期以来吸引了兴趣的概率，并导致了新的方法和理论的发展，丰富了数理统计和概率论。一个经典的例子是Kolmogorov-Smirnov统计量的渐近分布问题，它最终导致了弱收敛和强近似理论的发展。在未来几年的调查计划，集中他的努力大样本理论问题与特定泛函的经验分布。这些方法包括L1-范数密度估计过程、密度估计的积分泛函以及局部经验和U-统计过程。预期的结果应该有潜在的用途，在一类实用的拟合优度技术和统计估计的发展。事实上，这些研究已经产生了许多新的方法，以智能的方式评估和描述产生自然现象的基本机制的行为。

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.