Empirical likelihood, smoothed likelihood, and their applications

非参数似然方法，如经验似然法和平滑似然法在许多领域都是强有力的工具。它们是有效统计推断的强大框架，不会对数据施加参数模型。这对于具有复杂结构的数据特别有用。然而，提出适当的非参数似然方法，从复杂的科学设置的数据和研究相应的理论属性可能是非常具有挑战性的。在这方面有许多悬而未决的问题。我的研究涉及经验似然和平滑似然方法，以及它们在各种科学数据中的应用。该提案包括两个专题。

Nonparametric likelihood methods such as the empirical likelihood and the smoothed likelihood are powerful tools in many areas. They are powerful frameworks for valid statistical inference that do not impose a parametric model on the data. This is particularly useful for data with a complicated structure. However, proposing appropriate nonparametric likelihood methods for data from complex scientific settings and studying the corresponding theoretical properties can be very challenging. There are many open-ended problems in this area. My research is concerned with the empirical likelihood and smoothed likelihood methods, and their application to scientific data of various kinds. This proposal consists of two topics.