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Abstract We consider likelihood-ratio-type statistics for testing restrictions on parameters built from a convex M-estimation criterion. In general, these statistics are not asymptotically pivotal. We propose a general simple nonparametric bootstrap procedure that yields asymptotically valid critical and p-values. The method modifies the bootstrap objective function to mimic what happens under the null hypothesis. A Monte-Carlo study illustrates that our method controls…

Summary We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one step and relies on a unique regularisation parameter. We derive rates of the convergence for the estimator and its first derivative, which are uniform in the support of the endogenous variable. We also address the issue of imposing monotonicity in estimation and extend…

非参数回归模型的涵盖检验AI 解读

We set up a formal framework to characterize encompassing of nonparametric models through the $L^2$ distance. We contrast it to previous literature on the comparison of nonparametric regression models. We then develop testing procedures for the encompassing hypothesis that are fully nonparametric. Our test statistics depend on kernel regression, raising the issue of bandwidth’s choice. We investigate two alternative approaches to obtain a “small bias property” for our test…

线性工具变量模型中对识别强度稳健的非参数推断AI 解读

For a linear IV regression, we propose two new inference procedures on parameters of endogenous variables that are robust to any identification pattern, do not rely on a linear first-stage equation, and account for heteroskedasticity of unknown form. Building on Bierens (1982), we first propose an Integrated Conditional Moment (ICM) type statistic constructed by setting the parameters to the value under the null hypothesis. The ICM procedure tests at the same time the value…

半强识别下的条件矩模型AI 解读

We consider conditional moment models under semi-strong identification. Identification strength is directly defined through the conditional moments that flatten as the sample size increases. Our new minimum distance estimator is consistent, asymptotically normal, robust to semi-strong identification, and does not rely on the choice of a user-chosen parameter, such as the number of instruments or some smoothing parameter. Heteroskedasticity-robust inference is possible…

参数框架下的模型等价性检验AI 解读

In empirical research, one commonly aims to obtain evidence in favor of restrictions on parameters, appearing as an economic hypothesis, a consequence of economic theory, or an econometric modeling assumption. I propose a new theoretical framework based on the Kullback–Leibler information to assess the approximate validity of multivariate restrictions in parametric models. I construct tests that are locally asymptotically maximin and locally asymptotically uniformly most…

条件估计方程下的平滑最小距离估计与检验：带宽一致理论AI 解读

To study the influence of a bandwidth parameter in inference with conditional moments, we propose a new class of estimators and establish an asymptotic representation of our estimator as a process indexed by a bandwidth, which can vary within a wide range including bandwidths independent of the sample size. We study its behavior under misspecification. We also propose an efficient version of our estimator. We develop a procedure based on a distance metric statistic for…

一为众、众为一：多回归变量下的回归模型检验AI 解读

We develop a novel approach to building checks of parametric regression models when many regressors are present, based on a class of sufficiently rich semiparametric alternatives, namely single-index models. We propose an omnibus test based on the kernel method that performs against a sequence of directional nonparametric alternatives as if there was only one regressor whatever the number of regressors. This test can be viewed as a smooth version of the integrated…

摘要暂缺

We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local alternatives approaching the parametric model at a rate arbitrarily close to $1/\sqrt{n}$. Asymptotic critical values come from the standard normal distribution and the bootstrap can be used in…

回归模型非参数设定检验的最优极小极大速率AI 解读

In the context of testing the specification of a nonlinear parametric regression function, we adopt a nonparametric minimax approach to determine the maximum rate at which a set of smooth alternatives can approach the null hypothesis while ensuring that a test can uniformly detect any alternative in this set with some predetermined power. We show that a smooth nonparametric test has optimal asymptotic minimax properties for regular alternatives. As a by-product, we obtain…

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非参数回归中的变量显著性检验AI 解读

A procedure for testing the significance of a subset of explanatory variables in a nonparametric regression is proposed. Our test statistic uses the kernel method. Under the null hypothesis of no effect of the variables under test, we show that our test statistic has an nh p 2 /2 standard normal limiting distribution, where p 2 is the dimension of the complete set of regressors. Our test is one-sided, consistent against all alternatives and detects local alternatives…

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