A NONPARAMETRIC HELLINGER METRIC TEST FOR CONDITIONAL INDEPENDENCE

We propose a nonparametric test of conditional independence based on the weighted Hellinger distance between the two conditional densities, f(y|x,z) and f(y|x), which is identically zero under the null. We use the functional delta method to expand the test statistic around the population value and e...

Full description

Saved in:

Bibliographic Details
Published in:	Econometric theory 2008-08, Vol.24 (4), p.829-864
Main Authors:	Su, Liangjun, White, Halbert
Format:	Article
Language:	eng
Subjects:	Approximation Causality Density Density estimation Econometrics Economic models Estimators Exchange rates Hypotheses Mathematical functions Mathematical models Monte Carlo simulation Nonparametric tests Parameter estimation Probability theory Random variables Research Article Significance tests Stochastic processes Studies Weighting functions
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	We propose a nonparametric test of conditional independence based on the weighted Hellinger distance between the two conditional densities, f(y\|x,z) and f(y\|x), which is identically zero under the null. We use the functional delta method to expand the test statistic around the population value and establish asymptotic normality under β-mixing conditions. We show that the test is consistent and has power against alternatives at distance n−1/2h−d/4. The cases for which not all random variables of interest are continuously valued or observable are also discussed. Monte Carlo simulation results indicate that the test behaves reasonably well in finite samples and significantly outperforms some earlier tests for a variety of data generating processes. We apply our procedure to test for Granger noncausality in exchange rates.
ISSN:	0266-4666 1469-4360