arXiv 2 May 2025 · Econometrics
arXiv:2505.01161 · PDF · DOI · OpenAlex · Extracted main text
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Juan Carlos Escanciano (2024) A gaussian process approach to model checks | 1.000 | 8 | 4 | 100% |
| 2 | Krikamol Muandet, Wittawat Jitkrittum, and Jonas Kübler (2020) Kernel conditional moment test via maximum moment restriction | 1.000 | 6 | 3 | 100% |
| 3 | Herman J Bierens (1982) Consistent model specification tests | 0.843 | 3 | 3 | 100% |
| 4 | Miguel A Delgado, Manuel A Domńguez, and Pascal Lavergne (2006) Consistent tests of conditional moment restrictions | 0.843 | 3 | 3 | 100% |
| 5 | Juan Carlos Escanciano and Sze-Chuan Goh (2014) Specification analysis of linear quantile models | 0.843 | 3 | 3 | 100% |
| 6 | Pedro HC Sant’Anna and Xiaojun Song (2019) Specification tests for the propensity score | 0.644 | 2 | 2 | 100% |
| 7 | AW van der Vaart and Jon A Wellner (1997) Weak convergence and empirical processes with applications to statistics | 0.511 | 2 | 2 | 50% |
| 8 | Randall L Eubank and Clifford H Spiegelman (1990) Testing the goodness of fit of a linear model via nonparametric regression techniques | 0.511 | 2 | 1 | 100% |
| 9 | Hong-Wei Sun and Ding-Xuan Zhou (2008) Reproducing kernel hilbert spaces associated with analytic translation-invariant mercer kernels | 0.511 | 2 | 1 | 100% |
| 10 | Herman J Bierens and Werner Ploberger (1997) Asymptotic theory of integrated conditional moment tests | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 36 scored citations.