Testing for Conditional Mean Independence with Covariates through Martingale Difference Divergence

Ze Jin, Xiaohan Yan, David S. Matteson
Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, PMLR R16:1-11, 2018.

Abstract

A crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known effect Z, i.e., E(Y|X, Z) = E(Y|Z). Assuming that E(Y|Z) and Z are linearly related, we reformulate an equivalent notion of conditional mean independence through transformation, which is approximated in practice. We apply the martingale difference divergence (Shao and Zhang, 2014) to measure conditional mean dependence, and show that the estimation error from approximation is negligible, as it has no impact on the asymptotic distribution of the test statistic under some regularity assumptions. The implementation of our test is demonstrated by both simulations and a financial data example.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR16-jin18a, title = {Testing for Conditional Mean Independence with Covariates through Martingale Difference Divergence}, author = {Jin, Ze and Yan, Xiaohan and Matteson, David S.}, booktitle = {Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence}, pages = {1--11}, year = {2018}, editor = {Globerson, Amir and Silva, Ricardo}, volume = {R16}, series = {Proceedings of Machine Learning Research}, month = {06--10 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r16/main/assets/jin18a/jin18a.pdf}, url = {https://proceedings.mlr.press/r16/jin18a.html}, abstract = {A crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known effect Z, i.e., E(Y|X, Z) = E(Y|Z). Assuming that E(Y|Z) and Z are linearly related, we reformulate an equivalent notion of conditional mean independence through transformation, which is approximated in practice. We apply the martingale difference divergence (Shao and Zhang, 2014) to measure conditional mean dependence, and show that the estimation error from approximation is negligible, as it has no impact on the asymptotic distribution of the test statistic under some regularity assumptions. The implementation of our test is demonstrated by both simulations and a financial data example.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Testing for Conditional Mean Independence with Covariates through Martingale Difference Divergence %A Ze Jin %A Xiaohan Yan %A David S. Matteson %B Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2018 %E Amir Globerson %E Ricardo Silva %F pmlr-vR16-jin18a %I PMLR %P 1--11 %U https://proceedings.mlr.press/r16/jin18a.html %V R16 %X A crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known effect Z, i.e., E(Y|X, Z) = E(Y|Z). Assuming that E(Y|Z) and Z are linearly related, we reformulate an equivalent notion of conditional mean independence through transformation, which is approximated in practice. We apply the martingale difference divergence (Shao and Zhang, 2014) to measure conditional mean dependence, and show that the estimation error from approximation is negligible, as it has no impact on the asymptotic distribution of the test statistic under some regularity assumptions. The implementation of our test is demonstrated by both simulations and a financial data example. %Z Reissued by PMLR on 04 October 2026.
APA
Jin, Z., Yan, X. & Matteson, D.S.. (2018). Testing for Conditional Mean Independence with Covariates through Martingale Difference Divergence. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R16:1-11 Available from https://proceedings.mlr.press/r16/jin18a.html. Reissued by PMLR on 04 October 2026.

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