Empirical likelihood, smoothed likelihood, and their applications

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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.