TY - JOUR

T1 - On the least trimmed squares estimator

AU - Mount, David M.

AU - Netanyahu, Nathan S.

AU - Piatko, Christine D.

AU - Silverman, Ruth

AU - Wu, Angela Y.

PY - 2014/5

Y1 - 2014/5

N2 - The linear least trimmed squares (LTS) estimator is a statistical technique for fitting a linear model to a set of points. Given a set of n points in R d and given an integer trimming parameter h≤n, LTS involves computing the (d-1)-dimensional hyperplane that minimizes the sum of the smallest h squared residuals. LTS is a robust estimator with a 50 %-breakdown point, which means that the estimator is insensitive to corruption due to outliers, provided that the outliers constitute less than 50 % of the set. LTS is closely related to the well known LMS estimator, in which the objective is to minimize the median squared residual, and LTA, in which the objective is to minimize the sum of the smallest 50 % absolute residuals. LTS has the advantage of being statistically more efficient than LMS. Unfortunately, the computational complexity of LTS is less understood than LMS. In this paper we present new algorithms, both exact and approximate, for computing the LTS estimator. We also present hardness results for exact and approximate LTS. A number of our results apply to the LTA estimator as well.

AB - The linear least trimmed squares (LTS) estimator is a statistical technique for fitting a linear model to a set of points. Given a set of n points in R d and given an integer trimming parameter h≤n, LTS involves computing the (d-1)-dimensional hyperplane that minimizes the sum of the smallest h squared residuals. LTS is a robust estimator with a 50 %-breakdown point, which means that the estimator is insensitive to corruption due to outliers, provided that the outliers constitute less than 50 % of the set. LTS is closely related to the well known LMS estimator, in which the objective is to minimize the median squared residual, and LTA, in which the objective is to minimize the sum of the smallest 50 % absolute residuals. LTS has the advantage of being statistically more efficient than LMS. Unfortunately, the computational complexity of LTS is less understood than LMS. In this paper we present new algorithms, both exact and approximate, for computing the LTS estimator. We also present hardness results for exact and approximate LTS. A number of our results apply to the LTA estimator as well.

KW - Approximation algorithms

KW - Least trimmed squares estimator

KW - Linear estimation

KW - Lower bounds

KW - Robust estimation

UR - http://www.scopus.com/inward/record.url?scp=84896720133&partnerID=8YFLogxK

U2 - 10.1007/s00453-012-9721-8

DO - 10.1007/s00453-012-9721-8

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AN - SCOPUS:84896720133

SN - 0178-4617

VL - 69

SP - 148

EP - 183

JO - Algorithmica

JF - Algorithmica

IS - 1

ER -