Robust Regression and Outlier Detection

Ordinary least squares assumes that the data all lie near the fit line or plane, but depart from it by the addition of normally distributed residual values.

[2] The breakdown point of a robust regression method is the fraction of outlying data that it can tolerate while remaining accurate.

[1][5] Although the least median has an appealing geometric description (as finding a strip of minimum height containing half the data), its low efficiency leads to the recommendation that the least trimmed squares be used instead; least trimmed squares can also be interpreted as using the least median method to find and eliminate outliers and then using simple regression for the remaining data,[4] and approaches simple regression in its efficiency.

The sixth chapter concerns outlier detection, comparing methods for identifying data points as outliers based on robust statistics with other widely used methods, and the final chapter concerns higher-dimensional location problems as well as time series analysis and problems of fitting an ellipsoid or covariance matrix to data.

[6] Reviewers Seheult and Green complain that too much of the book acts as a user guide to the authors' software, and should have been trimmed.

[6] However, reviewer Gregory F. Piepel writes that "the presentation is very good", and he recommends the book to any user of statistical methods.

[1] And, while suggesting the reordering of some material, Karen Kafadar strongly recommends the book as a textbook for graduate students and a reference for professionals.