Penalized exponential series estimation of copula densities with an application to intergenerational dependence of body mass index

We propose a penalized maximum likelihood estimator of copula densities that is based on the multivariate exponential series density estimator. We employ an approximate likelihood cross validation method to select the smoothing parameter. We demonstrate the usefulness of the proposed method via Monte Carlo simulations. We apply this method to estimate copula densities between children’s and parents’ body mass indices (BMI). Our results suggest that the dependence relationship is generally asymmetric and stronger for females. We also find a higher intergenerational BMI dependence for low income families.