Empirical process theory concerns the study of empirical measures
P_n -- measures determined by samples -- and the convergence thereof
to the population or true probability distribution P as the sample
size n grows. One very useful mode of convergence for statistics
is uniform convergence over some large class of sets or functions,
and this leads to the study of maximal inequalities for empirical
Projects and Research Goals
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- Project 1: Bootstrapping M - estimators:
Project Description and Goals: This project aims to develop
ways of proving validity of the bootstrap method for M - estimators
of finite-dimensional and infinite-dimensional parameters. Models of
particular interest include models of recent interest in survival
analysis and censored data including double censoring, the
Ibragimov and Has'minskii or Vardi - Zhang models, and frailty models.
This project has aspects involving computational issues, since
rapid computation of the basic estimators is important to implementation
of the bootstrap.
- Project 2: Bootstrap and delta method:
Project Description and Goals: The goal of this project to
to establish asymptotic validity of the bootstrap for Hadamard
and Frechet differentiable functions and methods for verifying
Hadamard differentiability for a wide variety of examples in survival
analysis and high-dimensional data analysis.
- Project 3: Convergence rates in nonparametric estimation:
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