Problems on the Asymptotic Behavior of Functionals of the Empirical Distribution

关于经验分布泛函的渐近行为的Mason问题长期以来一直吸引着概率学家的兴趣，并导致了新方法和新理论的发展，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逼近理论的发展。在接下来的几年里，研究人员计划将他的精力集中在与经验分布的特定泛函有关的大样本理论问题上。其中包括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。预期的结果应该在开发一类实用的拟合优度技术和统计估计器方面具有潜在的用途。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潜在机制的行为。

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.