[PAST EVENT] Mathematics Colloquium and EXTREEMS-QED Lecture: Adam Jaeger (University of Georgia)
February 11, 2015
2pm - 3pm
Abstract: The likelihood function plays a pivotal role in statistical inference because it is easy to work with and the resultant estimators are known to have good properties. However, these results hinge on correct specification of the likelihood as the true data-generating mechanism. Many modern problems involve extremely complicated distribution functions, which may be difficult -- if not impossible -- to express explicitly. This is a serious barrier to the likelihood approach, which requires the specification of a model. Non-parametric methods are one way to avoid the problem of having to specify a particular data-generating mechanism, but can be computationally intensive reducing their accessibility for large data problems. We propose a new approach that combines multiple non-parametric likelihood-type objects to build a data-driven approximation of the true function. We build on two alternative likelihood approaches, empirical and composite likelihood, taking advantage of the strengths of each. Specifically, from empirical likelihood we borrow the ability to avoid a parametric specification, and from composite likelihood we gain a decrease in computational load. In this talk, I define the general form of the composite empirical likelihood, derive some of the asymptotic properties of this new class, and explore some applications of the approach.