Lu Yang, University of Minnesota

A New Dependence Measure for Mixed Outcomes

Lu Yang, University of Minnesota 

Abstract

The study of dependence among mixed continuous and multinomial outcomes is an important task in many areas. Despite the extensive study of dependence measures, there are many open issues when applying these established tools to mixed data. For instance, two associated mixed variables might have a Pearson correlation of nearly zero. Furthermore, many existing works primarily focus on independence tests rather than on properly measuring the strength of dependence, and how to characterize perfect dependence in mixed outcomes has not been addressed in the literature. We propose a novel dependence measure between a multinomial and a continuous variable. The measure is based on the Hellinger distance in the continuous variable among subpopulations defined by the values of the multinomial variable, which satisfies all the ideal properties of a dependence measure, without imposing distributional assumptions and outperforming existing measures. An estimator of the dependence measure and an independence test are proposed. The asymptotic distribution of the estimator has a closed-form expression, and thus we can construct confidence intervals and conduct independence tests without resorting to bootstrap.

Bio

Lu Yang is an Assistant Professor in the School of Statistics at the University of Minnesota. She received her Ph.D. in Statistics from the University of Wisconsin-Madison in 2017. Prior to joining UMN, she was an Assistant Professor in Actuarial Science and Mathematical Finance at the University of Amsterdam. Her overarching interests are in the development of statistical methodology motivated by insurance applications. Her current research focuses on multivariate analysis, nonparametric estimation of copulas, and regression model diagnostics, especially with discrete and semicontinuous outcomes.