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

首席研究员将继续利用 独立同列的表示 分布随机变量作为分位数的序列 独立同分布均匀观测函数 变量 分位数函数是左连续逆 分布函数。 此表示提供了一个 随机变量部分和之间的强联系 和经验过程。 首席研究员，沿着 与一些合作者，已经使用这种技术在过去的 几年来，我们得到了很多有趣的结果。 具体问题 包括基弗过程版本的加权 近似，Bahadur-Kiefer型过程的收敛性， 顺序统计量加权和的收敛性，并迭代 极值和的对数律。

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.