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Kernel Conditional Moment Test via Maximum Moment Restriction

Author

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  • Krikamol Muandet
  • Wittawat Jitkrittum
  • Jonas Kubler

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.

Suggested Citation

  • Krikamol Muandet & Wittawat Jitkrittum & Jonas Kubler, 2020. "Kernel Conditional Moment Test via Maximum Moment Restriction," Papers 2002.09225, arXiv.org, revised Jun 2020.
    • Handle: RePEc:arx:papers:2002.09225
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    References listed on IDEAS

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    Cited by:

    1. Nishanth Dikkala & Greg Lewis & Lester Mackey & Vasilis Syrgkanis, 2020. "Minimax Estimation of Conditional Moment Models," Papers 2006.07201, arXiv.org.
    2. Victor Chernozhukov & Whitney Newey & Rahul Singh & Vasilis Syrgkanis, 2020. "Adversarial Estimation of Riesz Representers," Papers 2101.00009, arXiv.org, revised Jan 2024.

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