Empirical Likelihood-Based Inference in Conditional Moment Restriction Models
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This paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions. Our estimator generalizes the maximum empirical likelihood estimator (MELE) of Qin and Lawless (1994). Using a kernel smoothing method, we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood-based procedure. This yields a one-step estimator which avoids estimating optimal instruments. Our likelihood ratio-type statistic for parametric restrictions does not require the estimation of variance, and achieves asymptotic pivotalness implicitly. The estimation and testing procedures we propose are normalization invariant. Simulation results suggest that our new estimator works remarkably well in finite samples.
核设定检验的数据驱动调参:选择渐近理论、有效性与功效
We develop model checks for conditional moment restrictions whose tuning parameters, the kernel bandwidth and the regularization level, are selected by cross-validation. The tests regress the estimated residuals on the covariates via kernel ridge regression (KRR), yielding a coefficient function in a reproducing kernel Hilbert space (RKHS) that vanishes under the null and is nonzero for any misspecification not annihilated by the Neyman projection. Our central contribution…
BLP 模型中的条件矩估计与推断
The random-coefficient demand model of Berry, Levinsohn, and Pakes (1995) is commonly estimated by the generalized method of moments (GMM), using an unconditional moment restriction with a fixed set of instruments. Identification of the model, however, rests on a conditional moment restriction. The two are not equivalent: the unconditional restriction may admit additional parameter values. We construct a counterexample in which the model is identified by the conditional…
协变量漂移下的非参数拟合优度检验
This paper develops procedures for nonparametric goodness-of-fit testing under covariate shift, where labelled data are drawn from a source population but goodness-of-fit is evaluated for a target population. The distribution mismatch is quantified by either a bounded moment condition or a sub-exponential tail condition on the target-to-source density ratio. Our method combines truncated importance-weighting kernel ridge regression with a multiplier bootstrap to construct…
非参数回归的稳健经验似然及其断点回归应用
Empirical likelihood serves as a powerful tool for constructing confidence intervals in nonparametric regression and regression discontinuity designs (RDD). The original empirical likelihood framework can be naturally extended to these settings using local linear smoothers, with Wilks' theorem holding only when an undersmoothed bandwidth is selected. However, the generalization of bias-corrected versions of empirical likelihood under more realistic conditions is non-trivial…
条件矩限制的局部稳健核设定检验
We develop kernel-based specification tests for semiparametric conditional moment models with high-dimensional nuisance parameters, extending existing conditional moment tests---which typically require asymptotically linear nuisance estimators---to accommodate modern machine-learning methods. The proposed locally robust kernel tests combine Neyman-orthogonal moments, cross-fitting, and reproducing kernel Hilbert space methods, yielding inference that is first-order…
条件矩约束下核最小距离估计与检验的统一框架
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…