Details: PROC ROBUSTREG :: SAS/STAT(R) 12.3 User's Guide

Details: ROBUSTREG Procedure

M Estimation
High-Breakdown-Value Estimation
MM Estimation
Robust Distance
Leverage Point and Outlier Detection
Implementation of the WEIGHT Statement
INEST= Data Set
OUTEST= Data Set
Computational Resources
ODS Table Names
ODS Graphics

This section describes the statistical and computational aspects of the ROBUSTREG procedure. The following notation is used throughout this section.

Let $\bX = (x_{ij})$ denote an $n\times p$ matrix, $\mb {y}=(y_1,\ldots ,y_ n)’$ denote a given n-vector of responses, and $\btheta = (\theta _1,\ldots ,\theta _ p)’$ denote an unknown p-vector of parameters or coefficients whose components are to be estimated. The matrix $\bX$ is called the design matrix. Consider the usual linear model

$\mb {y} = \bX \btheta + \mb {e}$

where $\mb {e} = (e_1,\ldots ,e_ n)’$ is an n-vector of unknown errors. It is assumed that (for a given $\bX$ ) the components of $\mb {e}$ are independent and identically distributed according to a distribution $L(\cdot / \sigma )$ , where $\sigma$ is a scale parameter (usually unknown). Often $L(\cdot ) \approx \Phi (\cdot )$ , the standard normal distribution function. The vector of residuals for a given value of $\hat\btheta$ is denoted by $\mb {r} = (r_1,\ldots ,r_ n)’$ and the ith row of the matrix $\bX$ is denoted by $\mb {x}_ i’$ .

The ROBUSTREG Procedure

Details: ROBUSTREG Procedure