Department seminar by Rakheon Kim

Please Note: This seminar will be given online.

Personalized Statistical Learning and Network Analysis with Sparsity for Actuarial Use

With ever increasing data for numerous variables being collected in insurance market, a key interest is to distinguish scientifically meaningful relationships between variables using sparsity, meaning that only a small number of relationships between variables are non-zero. In this talk, we discuss sparsity as an effective tool for personalized statistical learning and covariance network analysis. Specifically, in a linear model, the effects of predictors to the response may not be the same across all individuals. Such differentiated effects can be modeled by a varying-coefficient model. However, model selection of a varying-coefficient model is challenging when there is a pre-specified group structure among variables. We propose a novel model selection method to address such structured variables by exploiting sparsity through a hierarchical group penalty. On the other hand, in a covariance matrix, sparsity is useful to identify network structure between variable. However, current approaches to obtain a sparse covariance matrix do not yet guarantee positive definiteness or asymptotic efficiency, thus invalidating many statistical analyses or reducing confidence in estimation. We propose a new thresholding estimator which is always positive definite and asymptotically efficient with probability tending to one. We illustrate the performance of our proposed methods in numerical studies and discuss implications in actuarial modeling for pricing and risk management.