This section describes the statistical and computational aspects of the ROBUSTREG procedure. The following notation is used throughout this section.
Let denote an matrix, denote a given nvector of responses, and denote an unknown pvector of parameters or coefficients whose components are to be estimated. The matrix is called the design matrix. Consider the usual linear model

where is an nvector of unknown errors. It is assumed that (for a given ) the components of are independent and identically distributed according to a distribution , where is a scale parameter (usually unknown). Often , the standard normal distribution function. The vector of residuals for a given value of is denoted by and the ith row of the matrix is denoted by .