Title: Nonparametric testing of conditional independence using asymmetric kernels
Authors: Eduardo Fonseca Mendes - Fundacao Getulio Vargas (Brazil) [presenting]
Marcelo Fernandes - Sao Paulo School of Economics, FGV (Brazil)
Abstract: Statistical tools for testing conditional independence between $X$ and $Y$ given $Z$ are developed. In particular, we test whether the conditional density of $X$ given $Y$ and $Z$ is equal to the conditional density of $X$ given $Z$ only. We gauge the closeness between these conditional densities using a generalized entropic measure. To avoid degeneracy issues, we transform the variables of interest ($X,Y,Z$) to bound them in the unit interval, and then estimate their conditional densities using beta kernels. The latter are convenient because they are free of boundary bias. We show that our test statistics are asymptotically normal under the null hypothesis as well as under local alternatives. We assess the finite-sample properties of our entropic-based tests of conditional independence through Monte Carlo simulations.