A Modern Gauss-Markov Theorem

• 成果类型: Article
• 署名作者: Hansen, Bruce E.
• 署名单位: University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA19255
• 发表日期: 2022
• 页码: 1283-1294
• 关键词: asymptotic efficiency; linear-models; INFORMATION

摘要

This paper presents finite-sample efficiency bounds for the core econometric problem of estimation of linear regression coefficients. We show that the classical Gauss-Markov theorem can be restated omitting the unnatural restriction to linear estimators, without adding any extra conditions. Our results are lower bounds on the variances of unbiased estimators. These lower bounds correspond to the variances of the the least squares estimator and the generalized least squares estimator, depending on the assumption on the error covariances. These results show that we can drop the label linear estimator from the pedagogy of the Gauss-Markov theorem. Instead of referring to these estimators as BLUE, they can legitimately be called BUE (best unbiased estimators).