Nonparametric Conditional Copula Density Estimation With Applications to the Body Mass Index

ABSTRACT This study develops a nonparametric conditional copula density estimator that features a parametric carrier copula refined by an exponential series adjustment. We adopt the local likelihood approach for conditional distribution estimation and incorporate the influence of covariates via kernel smoothing. We further propose a method of tuning parameter selection for the conditional copula density estimation. Our numerical experiments demonstrate its superior performance. We provide two applications of the proposed method to two important public heath issues related to the body mass index (BMI). The first application provides new insight into the life‐cycle evolution of the interplay between BMI and hypertension and how it varies with gender. The second application reveals that the inter‐generational transmission of BMI, especially association in the upper tail region, is stronger for the lower income population.