Penalised variable selection with U-estimates

摘要

U-estimates are defined as maximisers of objective functions that are U-statistics. As an alternative to M-estimates, U-estimates have been extensively used in linear regression, classification, survival analysis, and many other areas. They may rely on weaker data and model assumptions and be preferred over alternatives. In this article, we investigate penalised variable selection with U-estimates. We propose smooth approximations of the objective functions, which can greatly reduce computational cost without affecting asymptotic properties. We study penalised variable selection using penalties that have been well investigated with M-estimates, including the LASSO, adaptive LASSO, and bridge, and establish their asymptotic properties. Generically applicable computational algorithms are described. Performance of the penalised U-estimates is assessed using numerical studies.