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Robust Regression Examples |
This section is based entirely on Rousseeuw and Van Zomeren (1990). Observations x_{i}, which are far away from most of the other observations, are called leverage points. One classical method inspects the Mahalanobis distances MD_{i} to find outliers x_{i}:
The definition of a leverage point is, therefore, based entirely on the outlyingness of x_{i} and is not related to the response value y_{i}. By including the y_{i} value in the definition, Rousseeuw and Van Zomeren (1990) distinguish between the following:
Rousseeuw and Van Zomeren (1990) propose to plot the standardized residuals of robust regression (LMS or LTS) versus the robust distances RD_{i} obtained from MVE. Two horizontal lines corresponding to residual values of +2.5 and -2.5 are useful to distinguish between small and large residuals, and one vertical line corresponding to the is used to distinguish between small and large distances.
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