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Kernel Minimum Distance Estimation and Testing with Conditional Moment Restrictions: A Unified Framework

Yuhao Li, Haokun Lu, Xiaojun Song

arXiv 18 Jul 2026 · Econometrics

arXiv:2607.16605 · PDF · Extracted main text

Abstract

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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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
1Pascal Lavergne and Valentin Patilea (2013) Smooth minimum distance estimation and testing with conditional estimating equations: uniform in bandwidth theory0.9507486%
2Manuel A Domńguez and Ignacio N Lobato (2004) Consistent estimation of models defined by conditional moment restrictions0.9416483%
3Manuel A Domńguez and Ignacio N Lobato (2015) A simple omnibus overidentification specification test for time series econometric models0.8558462%
4Krikamol Muandet, Wittawat Jitkrittum, and Jonas Kübler (2020) Kernel conditional moment test via maximum moment restriction0.81142100%
5Herman J Bierens and Werner Ploberger (1997) Asymptotic theory of integrated conditional moment tests0.7373367%
6Richard Blundell, Xiaohong Chen, and Dennis Kristensen (2007) Semi-nonparametric iv estimation of shape-invariant engel curves0.64441100%
7Krikamol Muandet, Kenji Fukumizu, Bharath Sriperumbudur, Bernhard Sc… (2017) Kernel mean embedding of distributions: A review and beyond0.64422100%
8Youngki Shin (2008) Semiparametric estimation of the box–cox transformation model0.58531100%
9Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo,… (2018) Double/debiased machine learning for treatment and structural parameters0.5113233%
10Whitney K Newey (1990) Efficient instrumental variables estimation of nonlinear models0.5113233%

Showing the top 10 of 44 scored citations.