Finite-sample distributions of the Wald, likelihood ratio, and Lagrange multiplier test statistics in the classical linear model. Issue 11 (3rd June 2017)

• Record Type: Journal Article
• Authors: Parker, Thomas
• Is Part Of: Communications in statistics. Volume 46:Issue 11(2017)
• Page Start: 5195
• Page End: 5202
• Publication Date: 2017-06-03
• Subjects: Finite-sample distribution -- Generalized beta distribution -- Linear regression model.; 62E15; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2015.1096397
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: In this note, it is shown that the finite-sample distributions of the Wald, likelihood ratio, and Lagrange multiplier statistics in the classical linear regression model are members of the generalized beta model introduced by McDonald and Xu (1995a ). This is useful for examining the properties of these test statistics. For example, this characterization makes it easy to find distribution, quantile, and density functions for each test statistic, makes it clear why Wald tests may overreject the null hypothesis using asymptotic critical values, and formalizes the fact that the Lagrange multiplier statistic follows a distribution with bounded support.