Likelihood Ratio Test in Multivariate Linear Regression: from Low to High Dimension

Likelihood Ratio Tests in Multivariate Linear Model

The aim of this paper is to review likelihood ratio test procedures in multivariate linear models, focusing on projection matrices. It is noted that the projection matrices to the spaces spanned by mean vectors in hypothesis and alternatives play an important role. Some basic properties are given for projection matrices. The models treated include multivariate regression model, discriminant ana...

From Multivariate to Functional Linear Regression

Abstract. The aim of this contribution is to present a new, however rapidly developing domain of statistics – functional data analysis (FDA). A particular problem of extending multivariate regression to the functional setting is discussed. First of all, two real data sets and connected problems are presented. Multivariate regression is briefly recalled focusing mainly on the case of strongly co...

Non linear robust regression in high dimension

Dimension reduction and coefficient estimation in multivariate linear regression

We introduce a general formulation for dimension reduction and coefficient estimation in the multivariate linear model. We argue that many of the existing methods that are commonly used in practice can be formulated in this framework and have various restrictions. We continue to propose a new method that is more flexible and more generally applicable. The method proposed can be formulated as a ...

Testing for Normality in the Linear Regression Model: an Empirical Likelihood Ratio Test

Author Contact: Lauren Dong, Statistics Canada; e-mail: [email protected]; FAX: (613) 951-3292 David Giles*, Dept. of Economics, University of Victoria, P.O. Box 1700, STN CSC, Victoria, B.C., Canada V8W 2Y2; e-mail: [email protected]; FAX: (250) 721-6214 * Corresponding co-author Abstract The empirical likelihood ratio (ELR) test for the problem of testing for normality in a linear regressi...