Linear least-squares regression can be very sensitive to unusual data. In this appendix to Fox and Weisberg (2011), we describe how to t several alternative robust-regression estimators, which attempt to down-weight or ignore unusual data: M -estimators; bounded-inuence estimators; MM -estimators; and quantile-regression estimators, including L1 regression. All estimation methods rely on assumptions for their validity. We say that an estimator or statistical procedure is robust if it provides useful information even if some of the assumptions used to justify the estimation method are not applicable. Most of this appendix concerns robust regression, estimation methods typically for the linear regression model that are insensitive to outliers and possibly high leverage points. Other types of robustness, for example to model misspecication, are not discussed here. These methods were developed between the mid-1960s and the mid-1980s. With the exception of the L1 methods described in Section 5, they are not widely used today.
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