Details

For the definition of Cook's distance, see [1]. For discussion of its use in detecting influential points in regression, see [2, 3].

Pages 67–68 of [2] suggest that observations with Cook's distances with values exceeding may be influential but that it is better to look at a plot of the Cook's distances versus with a benchmark line at .

Page 70 of [3] suggests looking at the half-normal plot of the Cook's distances to see those that are relatively large compared with the rest.

L1 Regression: minimizes the absolute sum of errors. This is computed using linear programming; see eqn. (3) in [4]. L1 regression is more robust than LS when moderate outliers are present, but it is still sensitive to extreme outliers.

RLINE: resistant regression line, discussed in §5 of [5], is based on medians.

[1] Cook's distance, Wikipedia.

[2] S. J. Sheather, A Modern Approach to Regression with R, New York: Springer, 2009.

[3] J. J. Faraway, Linear Models with R, Boca Raton: Chapman & Hall/CRC, 2005.

[4] S. C. Narula and J. F. Wellington, "The Minimum Sum of Absolute Errors Regression: A State of the Art Survey," International Statistical Review, 50(2), 1982 pp. 317–326.

[5] P. F. Velleman and D. C. Hoaglin, Applications, Basics and Computing of Exploratory Data Analysis, Boston: Duxbury Press, 1981.