A robust Liu regression estimator

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.

KEYWORDS:

• Liu estimator
• MM-estimates
• Partial least squares
• Partial robust M-estimator
• Robust estimator.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J07
• 62J05
• 62G35