Linear models with doubly exchangeable distributed errors.(English)Zbl 1270.62102

Summary: We study the general linear model (GLM) with doubly exchangeable distributed errors 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 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.

MSC:

 62J05 Linear regression; mixed models 62H12 Estimation in multivariate analysis 62F40 Bootstrap, jackknife and other resampling methods 62H10 Multivariate distribution of statistics
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