Robust Regression

Abstract

Consider the multivariate linear model

$$ {Y_i} = X_i^\prime \beta + {E_i},\quad \quad i = 1, \ldots ,n,$$

(9.1)

where Y _i : p×1 is the observation on the ith individual, X _i : q×p is the design matrix with known elements, β: q × 1 is a vector of unknown regression coefficients, and E _i : p × 1 is the unobservable random error that is usually assumed to be suitably centered and to have a p-variate distribution. A central problem in linear models is estimating the regression vector β.