Computing LTS Regression for Large Data Sets

Least trimmed squares (LTS) regression is based on the subset of h cases (out of n) whose least squares t possesses the smallest sum of squared residuals. The coverage h may be set between n=2 and n. The LTS method was proposed by Rousseeuw (1984, p. 876) as a highly robust regression estimator, with breakdown value (n ; h)=n. It turned out that the computation time of existing LTS algorithms grew too fast with the size of the data set, precluding their use for data mining. Therefore we develop a new algorithm called FAST-LTS. The basic ideas are an inequality involving order statistics and sums of squared residuals, and techniques which we call `selective iteration' and `nested extensions'. We also use an intercept adjustment technique to improve the precision. For small data sets FAST-LTS typically nds the exact LTS, whereas for larger data sets it gives more accurate results than existing algorithms for LTS and is faster by orders of magnitude. Moreover, FAST-LTS runs fas...

• Type: Journal
• Year: 2006
• Where: DATAMINE
• Authors: Peter Rousseeuw, Katrien van Driessen
• Keywords: Breakdown Value, DATAMINE 2006, Robust Regression, Robust Regression Estimator