The least trimmed differences regression estimator and alternatives

Arnold J. Stromberg, Ola Hössjer, Douglas M. Hawkins

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


This article proposes and studies the performance in theory and practice of the least trimmed differences (LTD) linear regression estimator. The estimator minimizes the sum of the smallest quartile of the squares of the differences in each pair of residuals. We obtain the breakdown point, maxbias curve, and large-sample properties of a class of estimators including the LTD as special case. The LTD estimator has a 50% breakdown point and Gaussian efficiency of 66%—substantially higher than other common high-breakdown estimators such as least median of squares and least trimmed squares. The LTD estimator is difficult to compute, but can be performed using a “feasible solution” algorithm. Half-sample jackknifing is effective in producing standard errors. In simulations we find the LTD to be more stable than other high-breakdown estimators. In an example, the LTD still shows instability like other high-breakdown estimators when there are small changes in the data.

Original languageEnglish
Pages (from-to)853-864
Number of pages12
JournalJournal of the American Statistical Association
Issue number451
StatePublished - Sep 1 2000


  • Robust high breakdown efficient estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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