具有相关数据的线性回归的经验风险最小化性能

IF 1 4区经济学 Q3 ECONOMICS

Econometric Theory Pub Date : 2023-11-10 DOI:10.1017/s0266466623000348

Christian Brownlees, Gu{dh}mundur Stef'an Gu{dh}mundsson

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引用次数: 0

摘要

本文建立了大维线性回归的经验风险最小化性能的界。我们通过允许数据是依赖的和重尾的来推广现有的结果。该分析涵盖了相同和非均匀分布观测值的情况。我们的分析是非参数的，因为回归量和回归量之间的关系没有指定。本文的主要结果表明，经验风险最小化器在依赖数据设置中实现了最佳性能(高达对数因子)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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PERFORMANCE OF EMPIRICAL RISK MINIMIZATION FOR LINEAR REGRESSION WITH DEPENDENT DATA

This paper establishes bounds on the performance of empirical risk minimization for large-dimensional linear regression. We generalize existing results by allowing the data to be dependent and heavy-tailed. The analysis covers both the cases of identically and heterogeneously distributed observations. Our analysis is nonparametric in the sense that the relationship between the regressand and the regressors is not specified. The main results of this paper show that the empirical risk minimizer achieves the optimal performance (up to a logarithmic factor) in a dependent data setting.

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来源期刊

Econometric Theory MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Since its inception, Econometric Theory has aimed to endow econometrics with an innovative journal dedicated to advance theoretical research in econometrics. It provides a centralized professional outlet for original theoretical contributions in all of the major areas of econometrics, and all fields of research in econometric theory fall within the scope of ET. In addition, ET fosters the multidisciplinary features of econometrics that extend beyond economics. Particularly welcome are articles that promote original econometric research in relation to mathematical finance, stochastic processes, statistics, and probability theory, as well as computationally intensive areas of economics such as modern industrial organization and dynamic macroeconomics.