  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 (GLM), 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 and is demonstrated with a variety of data
applications.
