In linear regression, an outlier is an observation with large residual. In other words, it is an observation whose dependent-variable value is unusual given its values on the predictor variables. An outlier observation may indicate a data entry error or other problem.
An observation with an extreme value on a predictor variable is a point with high leverage. Leverage is a measure of how far an independent variable deviates from its mean. These leverage points can have an effect on the estimate of regression coefficients.
Robust estimation for regression parameters deals with cases that have very high leverage, and cases that are outliers. Robust estimation is essentially a compromise between dropping the case(s) that are moderate outliers and seriously violating the assumptions of OLS regression. It is a form of weighted least squares regression and is done iteratively. At each step a new set of weights are determined based on the residuals. In general, the larger the residuals, the smaller the weights. So the weights depend on residuals. At the same time, the residuals depend on the model and the model depends on the weights .
By using empirical simulation approach with data generated from suggesting linear model and by making some of data points to be outlier observations, the comparisons was made between three robust estimation methods to study the differences in many cases and conditions between these estimation methods .
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