A family of adaptive robust estimates based on the symmetrical generalized logistic distribution

Abstract

A family of adaptive robust estimates which range from L₁ to L₂ estimates is suggested based on the symmetrical generalized logistic (SGL) distribution. Depending on whether existing outiiers and how serious for ihe outliers in sampling data, this adaptive SGL estimate family can automatically choose an L₂ estimate, L₁ estimate, or smoothed Huber estimate to fit the data. It is shown that the asymptotic efficiencies of the adaptive SGL estimates relative to L₂/L₁ estimates are 1 at the normal/Laplace distribution situations respectively. Practical examples show that the SGL estimates have satisfactory flexibility to deal with different patterns of outliers in data. Hence, the adaptive SGL robust estimates are useful for automatic analysis in systems identification and are very convenient for practitioners.

Keywords:

• Lestimate
• regression
• robust estimate
• symmcricoi generalized logistic