Linear Models with Doubly Exchangeable Distributed Errors

Abstract

We study the general linear model (GLM) with doubly exchangeable distributed error for m observed random variables. The doubly exchangeable general linear model (DEGLM) arises when the m-dimensional error vectors are “doubly exchangeable,” jointly normally distributed, which is a much weaker assumption than the independent and identically distributed error vectors as in the case of GLM or classical GLM (CGLM). We estimate the parameters in the model and also find their distributions. We show that the tests of intercept and slope are possible in DEGLM as a particular case using parametric bootstrap as well as multivariate Satterthwaite approximation.

Keywords:

• Doubly exchangeable covariance structure
• Linear model
• Multivariate Satterthwaite approximation
• Parametric bootstrap

2000 Mathematics Subject Classification:

• Primary 62J05, 62H15
• Secondary 62H12, 62H10

Acknowledgments

The authors thank Professor Thomas Mathew at the University of Maryland for his valuable and constructive suggestions for the hypotheses testing procedures in Sec. 5. The authors also thank two referees for their useful comments and suggestions. The first author thanks the support for the summer research grant from the College of Business at the University of Texas at San Antonio. The second author thanks the partial support by Financiamento Base 2010 ISFL-1-297 from FCT/MCTES/PT.