Mathematical Sciences: Empirical Processes and Statistical Applications

Jon A.Wellner将研究经验过程、统计学中的Bootstrap方法、半参数模型、反问题和非标准渐近性。研究内容包括无穷维M-估计的极限理论和相关的Bootstrap方法、一致Donsker函数类的保持定理、一致Bootstrap极限定理、单调函数和凸函数的估计、迭代凸子算法的收敛以及区间删失模型中整体泛函的行为。应用包括带协变量的双变量模型、区间截尾下的回归模型以及非参数极大似然估计量的研究。乔恩·A·威尔纳将进行统计学方面的研究。这项研究将涉及大(无限维)参数空间问题中新估计的大样本极限理论。

Jon A. Wellner will carry out research on empirical processes, bootstrap methods in statistics, semiparametric models, and inverse problems and nonstandard asymptotics. The research will involve limit theory for infinite - dimensional M - estimates and related bootstrap methods, preservation theorems for uniform Donsker classes of functions, uniform in $~P~$ bootstrap limit theorems, estimation of monotone and convex functions, convergence of iterative convex minorant algorithms, and the behavior of global functionals in models with interval censoring. Applications include bivariate models with covariates, regression models under interval censoring, and studies of nonparametric maximum likelihood estimators. Jon A. Wellner will carry out research in statistics. The research will involve large sample limit theory for new estimators in problems with large (infinite - dimensional) parameter spaces.