4:00pm - 4:30pm: Boyi Hu, UBC Statistics M.Sc. student
Title: An R package for monitoring test under density ratio model and its applications
Abstract: Quantiles and their functions are important population characteristics in many applications. In forestry, lower quantiles of the modulus of rapture and other mechanical properties of the wood products are important quality indices. It is important to ensure that the wood products in the market over the years meet the established industrial standards. Two well-known risk measures in finance and hydrology, value at risk (VaR) and median shortfall (MS), are extreme quantiles of their corresponding marginal distributions. Chen et al.  developed an empirical likelihood approach based on density ratio model and multiple samples. Following their work, we build a user-friendly R package to make their methods easy-to-use for practitioners. The package also includes some diagnostic tools to allow users to investigate the goodness of the fit of the density ratio model. With the help of this package, we study the performance of DRM CEL-based inference with clustered data with possibly different cluster sizes.
4:30pm - 5:00pm: Wayne Wang, UBC Statistics M.Sc. student
Title: Applying record value theory in combinatorial optimization with application to environmental statistics
Abstract: We consider the problem of optimal subset selection from a set of correlated random variables. In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive semidefinite matrix that characterizes the chosen subset. This problem arises in many domains, such as experimental designs, regression modelling, and environmental statistics. In this thesis, we attempt to establish an efficient polynomial-time algorithm for approximating the optimal solution to the problem. Firstly, we employ determinantal point processes, a special class of spatial point processes, to develop an easy-to-implement sampling-based stochastic search algorithm for the task of finding approximations to the combinatorial optimization problem. Secondly, we establish theoretical tools for assessing the quality of those approximations using statistical results from record value theory, the study of record values and related statistics from a sequence of observations.