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Model Checks in a Kernel Ridge Regression Framework

Yuhao Li

arXiv 2 May 2025 · Econometrics

arXiv:2505.01161 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We propose new reproducing kernel-based tests for model checking in conditional moment restriction models. By regressing estimated residuals on kernel functions via kernel ridge regression (KRR), we obtain a coefficient function in a reproducing kernel Hilbert space (RKHS) that is zero if and only if the model is correctly specified. We introduce two classes of test statistics: (i) projection-based tests, using RKHS inner products to capture global deviations, and (ii) random location tests, evaluating the KRR estimator at randomly chosen covariate points to detect local departures. The tests are consistent against fixed alternatives and sensitive to local alternatives at the $n^{-1/2}$ rate. When nuisance parameters are estimated, Neyman orthogonality projections ensure valid inference without repeated estimation in bootstrap samples. The random location tests are interpretable and can visualize model misspecification. Simulations show strong power and size control, especially in higher dimensions, outperforming existing methods.

Citation extraction

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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
1Juan Carlos Escanciano (2024) A gaussian process approach to model checks1.00084100%
2Krikamol Muandet, Wittawat Jitkrittum, and Jonas Kübler (2020) Kernel conditional moment test via maximum moment restriction1.00063100%
3Herman J Bierens (1982) Consistent model specification tests0.84333100%
4Miguel A Delgado, Manuel A Domńguez, and Pascal Lavergne (2006) Consistent tests of conditional moment restrictions0.84333100%
5Juan Carlos Escanciano and Sze-Chuan Goh (2014) Specification analysis of linear quantile models0.84333100%
6Pedro HC Sant’Anna and Xiaojun Song (2019) Specification tests for the propensity score0.64422100%
7AW van der Vaart and Jon A Wellner (1997) Weak convergence and empirical processes with applications to statistics0.5112250%
8Randall L Eubank and Clifford H Spiegelman (1990) Testing the goodness of fit of a linear model via nonparametric regression techniques0.51121100%
9Hong-Wei Sun and Ding-Xuan Zhou (2008) Reproducing kernel hilbert spaces associated with analytic translation-invariant mercer kernels0.51121100%
10Herman J Bierens and Werner Ploberger (1997) Asymptotic theory of integrated conditional moment tests0.40511100%

Showing the top 10 of 36 scored citations.