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On influence diagnostics in elliptical multivariate regression models with equicorrelated random errors
Institution:1. Departamento de Estadística, Universidad de Valparaíso, Chile;2. Departamento de Estatística, Universidade de São Paulo, Brazil;3. Pontificia Universidad Católica de Chile, Chile;1. Department of Statistics and Biostatistics, Rutgers University, Piscataway, NJ 08854, USA;2. Department of Biostatistics, Yale University, School of Public Health, New Haven, CT 06511, USA;3. Independent Consultant, Sudbury, MA 01776, USA;1. School of Science, Tianjin University of Commerce, Tianjin 300134, China;2. Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken NJ 07030, USA;1. Université libre de Bruxelles, ECARES and Département de Mathématique, Avenue F. D. Roosevelt, 50, CP 114/04, B-1050 Brussels, Belgium;2. Université libre de Bruxelles, ECARES and Département de Mathématique, Campus de la Plaine, Boulevard du Triomphe, CP 210, B-1050 Brussels, Belgium;1. Purdue University, United States;2. North Carolina State University, United States;3. Newcastle University, UK;1. Laboratoire de Mathématiques Appliquées de Compiègne-L.M.A.C., Université de Technologie de Compiègne, B.P. 529, 60205 Compiègne Cedex, France;2. L.S.T.A., Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France
Abstract:In this paper we discuss estimation and diagnostic procedures in elliptical multivariate regression models with equicorrelated random errors. Two procedures are proposed for the parameter estimation and the local influence curvatures are derived under some usual perturbation schemes to assess the sensitivity of the maximum likelihood estimates (MLEs). Two motivating examples preliminarily analyzed under normal errors are reanalyzed considering appropriate elliptical distributions. The local influence approach is used to compare the sensitivity of the model estimates.
Keywords:Multivariate model  Elliptical distribution  Equicorrelation matrix  Local influence
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