Mathematical Sciences: Empirical Processes and Statistical Applications

数学科学：经验过程和统计应用

• 批准号: 9306809
• 负责人: Jon Wellner
• 金额: $ 6万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9306809&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Empirical; Processes; Statistical

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.

乔恩·A Wellner将进行经验过程，统计，半参数模型，反问题和非标准渐近的自助方法的研究。 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，一致的$~P~$ Bootstrap极限定理，单调函数和凸函数的估计，迭代凸次子式算法的收敛性，以及区间删失模型中全局泛函的性质。 应用包括二元模型与协变量，区间删失下的回归模型，和非参数最大似然估计的研究。 乔恩·A维尔纳将进行统计研究。 该研究将涉及大样本极限理论的新估计问题与大（无限维）参数空间。