Unified robust estimation

Music City Center 

Robust estimation is primarily concerned with providing reliable parameter estimates in the
presence of outliers. Numerous robust loss functions have been proposed in regression and
classification, along with various computing algorithms. In modern penalised generalised
linear models (GLMs), however, there is limited research on robust estimation that can
provide weights to determine the outlier status of the observations. This article proposes
a unified framework based on a large family of loss functions, a composite of concave
and convex functions (CC-family). Properties of the CC-family are investigated, and CC-
estimation is innovatively conducted via the iteratively reweighted convex optimisation
(IRCO), which is a generalisation of the iteratively reweighted least squares in robust
linear regression. For robust GLM, the IRCO becomes the iteratively reweighted GLM.
The unified framework contains penalised estimation and robust support vector machine
(SVM) and is demonstrated with a variety of data applications.

robust

MM algorithm

variable selection

SVM

iteratively reweighted

GLM 

International Chinese Statistical Association