Robust Estimators for the Parameters of Simple Linear Regression Model with Replications

This paper deaIs with the problem of estimation of slope and intercept parameters of the simple linear regression model in the presence of outliers when repeated runs of observations are available. Various robust estimators are proposed that are based on a new method called Two Phases Method; where in phase-1 we simply employ, at each fix value of the independent variable, one of the robust methods of estimation of the location parameters to estimate the unknown value of the dependent variable. While, at phase-2 the reduced new observations obtained by phase-1 will be used to estimate the slope and intercept parameters by either the ordinary least squares results show the superiority of the suggested method of the usual least squares of robust method.