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 *n*-vector of responses, and denote an unknown *p*-vector 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 *n*-vector of unknown errors. It is assumed that (for a given *X*) the components of *e* 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 *i*th row of the matrix *X* is denoted by .