具有条件矩限制的核最小距离估计与检验：一个统一框架
Kernel Minimum Distance Estimation and Testing with Conditional Moment Restrictions: A Unified Framework
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中文总结 AI 辅助
该研究提出统一的核最小距离框架，用于估计和检验条件矩限制模型。通过嵌入条件矩构造V统计量目标函数，建立估计量性质及检验方法，推导检验统计量渐近性质，证明乘子自助法有效，模拟结果和实例分析展示了框架性能。
中文摘要 AI 辅助
我们提出了一个统一的核最小距离（KMD）框架，用于估计和检验由条件矩限制定义的模型。通过将条件矩嵌入再生核希尔伯特空间（RKHS），我们构造了一个封闭形式的V统计量目标函数，以量化与限制的距离。我们建立了相关最小距离估计量的\(\sqrt{n}\)一致性和渐近正态性。在此框架内，最小化的目标函数自然产生一个一致的综合规范检验。与基于投影的方法不同，我们的检验通过投影核结构固有地捕捉估计效应。我们推导了在原假设、备择假设和以参数速率\(n^{-1/2}\)收敛到原假设的一系列局部备择假设下检验统计量的渐近性质。建立了计算简单的乘子自助法的有效性以促进推断。模拟结果表明了稳健的有限样本性能，并通过使用英国家庭支出调查数据分析恩格尔曲线来说明该框架。
英文摘要
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.
