Influence analysis with homogeneous linear restrictions

Authors:
Klaus L. P. Vasconcellos;L. M. Zea Fernandez
Affiliations:
Departamento de Estatística, CCEN, Universidade Federal de Pernambuco, Cidade Universitária, 50740-540, Recife, PE, Brazil;Departamento de Estatística, CCEN, Universidade Federal de Pernambuco, Cidade Universitária, 50740-540, Recife, PE, Brazil
Venue:
Computational Statistics & Data Analysis
Year:
2009

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Abstract

We discuss the problem of influence analysis for the particular situation in which the observations must satisfy a set of homogeneous linear restrictions. We present the proof of a theoretical result showing, that for this situation, we can define a system of orthogonal influence directions, as in the unrestricted problem. As an illustration, we discuss a linear regression model where some of the explanatory variables are in the form of proportions, giving also an example with a numerical data set. Our example shows that the influence measure that is here discussed can be quite effective in identifying relevant perturbations.