似然模型中的正交矩
Orthogonal Moments in Likelihood Models
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中文总结 AI 辅助
针对含大量冗余参数的似然模型，提出利用正交矩构造对冗余参数不敏感的估计方程，以缓解附带参数问题，并在三类模型中给出显式构造。
中文摘要 AI 辅助
许多模型，例如针对面板数据或网络数据的固定效应模型，由于包含数量众多且估计不精确的冗余参数而难以估计。这通常会在感兴趣参数的估计量中引发附带参数问题。通过使用其期望对冗余参数值不敏感的估计方程，可以缓解该问题。我们讨论并对比了在似然模型背景下三种不敏感性的概念，也称为正交性：奈曼正交性、q阶奈曼正交性以及完全正交性。正交矩是通过将估计方程投影到嵌套子空间上获得的，这些子空间分别由冗余参数的得分、似然比关于冗余参数的前q阶导数以及模型的所有似然比张成。我们在二元选择、计数数据和非线性回归模型中给出了显式构造。
英文摘要
Many models, such as fixed-effect models for panel or network data, are hard to estimate because they feature nuisance parameters that are both numerous and estimated imprecisely. This, in general, causes an incidental-parameter problem in the estimator of the parameters of interest. The problem can be alleviated by working with an estimating equation whose expectation is insensitive to the value of the nuisance parameters. We discuss and contrast three notions of insensitivity, also called orthogonality, in the context of likelihood models: Neyman orthogonality, Neyman orthogonality to order q, and full orthogonality. Orthogonal moments are obtained by projecting the estimating equation on nested subspaces, which are spanned by, respectively, the scores of the nuisance parameters, the first q derivatives of the likelihood ratio with respect to the nuisance parameters, and all likelihood ratios of the model. We give explicit constructions in binary-choice, count-data, and nonlinear regression models.
发表机构
- University of Chicago（芝加哥大学）
- Toulouse School of Economics, Université Toulouse Capitole（图卢兹经济学院，图卢兹第三大学）
- Department of Economics, University College London（伦敦大学学院经济学系）
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