Kernel Conditional Moment Test via Maximum Moment Restriction

Krikamol Muandet, Wittawat Jitkrittum, Jonas Kübler
Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR 124:41-50, 2020.

Abstract

We propose a new family of specification tests called kernel conditional moment (KCM) tests. Our tests are built on a novel representation of conditional moment restrictions in a reproducing kernel Hilbert space (RKHS) called conditional moment embedding (CMME). After transforming the conditional moment restrictions into a continuum of unconditional counterparts, the test statistic is defined as the maximum moment restriction (MMR) within the unit ball of the RKHS. We show that the MMR not only fully characterizes the original conditional moment restrictions, leading to consistency in both hypothesis testing and parameter estimation, but also has an analytic expression that is easy to compute as well as closed-form asymptotic distributions. Our empirical studies show that the KCM test has a promising finite-sample performance compared to existing tests.

Cite this Paper

BibTeX
@InProceedings{pmlr-v124-muandet20a, title = {Kernel Conditional Moment Test via Maximum Moment Restriction}, author = {Muandet, Krikamol and Jitkrittum, Wittawat and K\"{u}bler, Jonas}, booktitle = {Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI)}, pages = {41--50}, year = {2020}, editor = {Peters, Jonas and Sontag, David}, volume = {124}, series = {Proceedings of Machine Learning Research}, month = {03--06 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v124/muandet20a/muandet20a.pdf}, url = {https://proceedings.mlr.press/v124/muandet20a.html}, abstract = {We propose a new family of specification tests called kernel conditional moment (KCM) tests. Our tests are built on a novel representation of conditional moment restrictions in a reproducing kernel Hilbert space (RKHS) called conditional moment embedding (CMME). After transforming the conditional moment restrictions into a continuum of unconditional counterparts, the test statistic is defined as the maximum moment restriction (MMR) within the unit ball of the RKHS. We show that the MMR not only fully characterizes the original conditional moment restrictions, leading to consistency in both hypothesis testing and parameter estimation, but also has an analytic expression that is easy to compute as well as closed-form asymptotic distributions. Our empirical studies show that the KCM test has a promising finite-sample performance compared to existing tests.} }
Endnote
%0 Conference Paper %T Kernel Conditional Moment Test via Maximum Moment Restriction %A Krikamol Muandet %A Wittawat Jitkrittum %A Jonas Kübler %B Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI) %C Proceedings of Machine Learning Research %D 2020 %E Jonas Peters %E David Sontag %F pmlr-v124-muandet20a %I PMLR %P 41--50 %U https://proceedings.mlr.press/v124/muandet20a.html %V 124 %X We propose a new family of specification tests called kernel conditional moment (KCM) tests. Our tests are built on a novel representation of conditional moment restrictions in a reproducing kernel Hilbert space (RKHS) called conditional moment embedding (CMME). After transforming the conditional moment restrictions into a continuum of unconditional counterparts, the test statistic is defined as the maximum moment restriction (MMR) within the unit ball of the RKHS. We show that the MMR not only fully characterizes the original conditional moment restrictions, leading to consistency in both hypothesis testing and parameter estimation, but also has an analytic expression that is easy to compute as well as closed-form asymptotic distributions. Our empirical studies show that the KCM test has a promising finite-sample performance compared to existing tests.
APA
Muandet, K., Jitkrittum, W. & Kübler, J.. (2020). Kernel Conditional Moment Test via Maximum Moment Restriction. Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), in Proceedings of Machine Learning Research 124:41-50 Available from https://proceedings.mlr.press/v124/muandet20a.html.

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