面板回归模型的核范数正则化估计

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摘要翻译：
本文研究了具有交互固定效应的面板回归模型。提出了两种新的基于凸目标函数最小化的估计方法。第一种方法用核（迹）范数正则化使残差平方和最小。第二种方法最小化残差的核范数。我们建立了两个结果估计量的相合性。与现有的最小二乘估计相比，这些估计具有非常重要的计算优势，因为它们被定义为凸目标函数的极小值。此外，核范数惩罚有助于解决交互固定效应模型的潜在辨识问题，特别是当回归子是低阶的且因子个数未知时。我们还证明了如何用核范数正则化或极小化估计作为有限个LS最小化迭代步骤的初值，构造与Bai(2009)和Moon and Weidner(2017)中的最小二乘(LS)估计渐近等价的估计。这种迭代避免了任何非凸极小化，而原来的LS估计问题一般是非凸的，可以有多个局部极小值。
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英文标题：
《Nuclear Norm Regularized Estimation of Panel Regression Models》
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作者：
Hyungsik Roger Moon, Martin Weidner
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最新提交年份：
2019
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
--

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英文摘要：
  In this paper we investigate panel regression models with interactive fixed effects. We propose two new estimation methods that are based on minimizing convex objective functions. The first method minimizes the sum of squared residuals with a nuclear (trace) norm regularization. The second method minimizes the nuclear norm of the residuals. We establish the consistency of the two resulting estimators. Those estimators have a very important computational advantage compared to the existing least squares (LS) estimator, in that they are defined as minimizers of a convex objective function. In addition, the nuclear norm penalization helps to resolve a potential identification problem for interactive fixed effect models, in particular when the regressors are low-rank and the number of the factors is unknown. We also show how to construct estimators that are asymptotically equivalent to the least squares (LS) estimator in Bai (2009) and Moon and Weidner (2017) by using our nuclear norm regularized or minimized estimators as initial values for a finite number of LS minimizing iteration steps. This iteration avoids any non-convex minimization, while the original LS estimation problem is generally non-convex, and can have multiple local minima.
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PDF链接：
https://arxiv.org/pdf/1810.10987

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关键词：面板回归 回归模型 正则化 econometrics fixed effect 正则 因子 解决 具有 minimizes