Generalized Cross Entropy Method for estimating joint distribution from incomplete information

Abstract

Obtaining a full joint distribution from individual marginal distributions with incomplete information is a non-trivial task that continues to challenge researchers from various domains including economics, demography, and statistics. In this work, we develop a new methodology referred to as ‘Generalized Cross Entropy Method’ (GCEM) that is aimed at addressing the issue. The objective function is proposed to be a weighted sum of divergences between joint distributions and various references. We show that the solution of the GCEM is unique and global optimal. Furthermore, we illustrate the applicability and validity of the method by utilizing it to recover the joint distribution of a household profile of a given administrative region. In particular, we estimate the joint distribution of the household size, household dwelling type, and household home ownership in Singapore. Results show a high-accuracy estimation of the full joint distribution of the household profile under study. Finally, the impact of constraints and weight on the estimation of joint distribution is explored.