Unified Robust Estimation via the COCO
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Robust estimation is concerned with how to provide reliable parameter estimates in the presence of outliers. Numerous robust loss functions have been proposed in regression and classification, along with various computing algorithms. This article proposes a unified framework for loss function construction and parameter estimation. The CC-family contains composite of concave and convex functions. The properties of the CC-family are investigated, and CC-estimation is innovatively conducted via composite optimization by conjugation operator (COCO). The weighted estimators are simple to implement, demonstrate robust quality in penalized generalized linear models and support vector machines, and can be conveniently extended to even more broad applications with existing software.
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