A robust Liu regression estimator

Filzmoser P., KURNAZ F. S.

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, vol.47, no.2, pp.432-443, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.1080/03610918.2016.1271889
  • Journal Name: COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.432-443
  • Keywords: Liu estimator, MM-estimates, Partial least squares, Partial robust M-estimator, Robust estimator, RIDGE-REGRESSION, SQUARES
  • Yıldız Technical University Affiliated: Yes

Abstract

The least-squares regression estimator can be very sensitive in the presence of multicollinearity and outliers in the data. We introduce a new robust estimator based on the MM estimator. By considering weights, also the resulting MM-Liu estimator is highly robust, but also the estimation of the biasing parameter is robustified. Also for high-dimensional data, a robust Liu-type estimator is introduced, based on the Partial Robust M-estimator. Simulation experiments and a real dataset show the advantages over the standard estimators and other robustness proposals.