Multivariate Linear L1 Regression for Cluster-Correlated Data

• Activity Number: 575
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jaakko Nevalainen*+ and Klaus Nordhausen and Hannu Oja
• Companies: University of Turku and University of Tampere and University of Tampere
• Keywords: clustered data ; L1 objective function ; spatial sign

Abstract

We consider the multivariate linear regression model with a p-variate response variable, q-variate vector of explanatory variables and a p-variate random error. The goal is to make inference on the unknown q x p regression coefficient matrix. Commonly, the estimation of the parameters is based on L2 or L1 objective functions. However, the standard assumption of the independence of the random errors does not hold if the data are clustered; they are correlated. In this talk we review the multivariate L1 regression theory in the case of iid error variables, and then we extend the asymptotic theory to the cluster-correlated case, including weighted L1 estimates of regression coefficients. The theory is illustrated with data examples and a simulation study.