Yuhao Li, Haokun Lu, Xiaojun Song
arXiv 18 Jul 2026 · Econometrics
arXiv:2607.16605 · PDF · Extracted main text
We propose a unified Kernel Minimum Distance (KMD) framework for estimating and testing models defined by conditional moment restrictions. By embedding conditional moments into a Reproducing Kernel Hilbert Space (RKHS), we construct a closed-form $V$-statistic objective function that quantifies the distance from the restrictions. We establish the $\sqrt{n}$-consistency and asymptotic normality of the associated minimum distance estimator. Within this framework, the minimized objective function naturally yields a consistent omnibus specification test. Unlike projection-based methods that require auxiliary nonparametric estimation for Neyman orthogonalization, our test inherently captures the estimation effect via a projected kernel structure. We derive asymptotic properties of the test statistics under the null hypothesis, the alternative hypothesis, and a sequence of local alternatives converging to the null at the parametric rate $n^{-1/2}$. The validity of a computationally simple multiplier bootstrap is established to facilitate inference. Simulation results demonstrate robust finite-sample performance, and the framework is illustrated by analyzing Engel curves using UK Family Expenditure Survey data.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Pascal Lavergne and Valentin Patilea (2013) Smooth minimum distance estimation and testing with conditional estimating equations: uniform in bandwidth theory | 0.950 | 7 | 4 | 86% |
| 2 | Manuel A Domńguez and Ignacio N Lobato (2004) Consistent estimation of models defined by conditional moment restrictions | 0.941 | 6 | 4 | 83% |
| 3 | Manuel A Domńguez and Ignacio N Lobato (2015) A simple omnibus overidentification specification test for time series econometric models | 0.855 | 8 | 4 | 62% |
| 4 | Krikamol Muandet, Wittawat Jitkrittum, and Jonas Kübler (2020) Kernel conditional moment test via maximum moment restriction | 0.811 | 4 | 2 | 100% |
| 5 | Herman J Bierens and Werner Ploberger (1997) Asymptotic theory of integrated conditional moment tests | 0.737 | 3 | 3 | 67% |
| 6 | Richard Blundell, Xiaohong Chen, and Dennis Kristensen (2007) Semi-nonparametric iv estimation of shape-invariant engel curves | 0.644 | 4 | 1 | 100% |
| 7 | Krikamol Muandet, Kenji Fukumizu, Bharath Sriperumbudur, Bernhard Sc… (2017) Kernel mean embedding of distributions: A review and beyond | 0.644 | 2 | 2 | 100% |
| 8 | Youngki Shin (2008) Semiparametric estimation of the box–cox transformation model | 0.585 | 3 | 1 | 100% |
| 9 | Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo,… (2018) Double/debiased machine learning for treatment and structural parameters | 0.511 | 3 | 2 | 33% |
| 10 | Whitney K Newey (1990) Efficient instrumental variables estimation of nonlinear models | 0.511 | 3 | 2 | 33% |
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