Mathematical Sciences: Empirical Processes and Statistical Applications

Jon A. Wellner将研究经验过程，统计中的自举方法，半参数模型，逆问题和非标准渐近。本研究将涉及无限维M -估计的极限理论及相关的自举方法，一致Donsker函数类的保存定理，一致的$~P~$自举极限定理，单调函数和凸函数的估计，迭代凸小算法的收敛性，以及区间截断模型中全局泛函的行为。应用包括带协变量的双变量模型，区间筛选下的回归模型，以及非参数极大似然估计的研究。Jon A. Wellner将进行统计学方面的研究。本研究将涉及大（无限维）参数空间问题中新估计量的大样本极限理论。

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.