EconBase
← All papers

Kernel Conditional Moment Test via Maximum Moment Restriction

Krikamol Muandet, Wittawat Jitkrittum, Jonas Kübler

arXiv 21 Feb 2020 · Mathematics — Statistics Theory · 6 citations (OpenAlex)

arXiv:2002.09225 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

56
references
141
in-text mentions
56
distinct cited
0
self-citations
8,927
main-text words

appendix boundary found by appendix_command · 66% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1M. Delgado, M. Domínguez, and P. Lavergne (2006) Consistent tests of conditional moment restrictions1.00073100%
2Q. Liu, J. Lee, and M. Jordan (2016) A kernelized Stein discrepancy for goodness-of-fit tests1.00073100%
3H. Bierens (1982) Consistent model specification tests1.00063100%
4K. Chwialkowski, H. Strathmann, and A. Gretton (2016) A kernel test of goodness of fit1.00053100%
5A. Hall (2005) Generalized Method of Moments0.9416483%
6I. Steinwart and A. Christmann (2008) Support Vector Machines0.9285380%
7A. Bennett, N. Kallus, and T. Schnabel (2019) Deep generalized method of moments for instrumental variable analysis0.7946350%
8G. Lewis and V. Syrgkanis (2018) Adversarial generalized method of moments0.7946350%
9M. Carrasco and J.-P. Florens (2000) Generalization of GMM to a continuum of moment conditions0.7373367%
10K. Muandet, K. Fukumizu, B. Sriperumbudur, and B. Schölkopf (2017) Kernel mean embedding of distributions: A review and beyond0.7373367%

Showing the top 10 of 56 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
10.5mm Model Checks in a Kernel Ridge Regression Framework 0.25mm1.00063
20.5mm A Powerful Chi-Square Specification Test with Support Vectors 0.25mm0.81142
3Kernel Minimum Distance Estimation and Testing with Conditional Moment Restrictions: A Unified Framework0.81142
4Minimax Estimation of Conditional Moment Models0.73753
50.5mm Finite-Sample Distortion in Kernel Specification Tests: A Perturbation Analysis of Empirical Directional Components 0.25mm0.51121
6Dual Instrumental Variable Regression0.40511
7Unified Inference on Moment Restrictions with Nuisance Parameters0.40511
8Automatic Debiased Machine Learning of Structural Parameters with General Conditional Moments0.40511