Model selection consistency of U-statistics with convex loss and weighted lasso penalty. Issue 4 (2nd October 2017)

• Record Type: Journal Article
• Authors: Rejchel, W.
• Is Part Of: Journal of nonparametric statistics. Volume 29:Issue 4(2017)
• Page Start: 768
• Page End: 791
• Publication Date: 2017-10-02
• Subjects: Convex loss function -- lasso penalty -- model selection consistency -- oracle -- ranking problem -- U-statistics; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2017.1369078
• Languages: English
• ISSNs: 1048-5252

Abstract

ABSTRACT: In the paper we consider minimisation of U -statistics with the weighted Lasso penalty and investigate their asymptotic properties in model selection and estimation. We prove that the use of appropriate weights in the penalty leads to the procedure that behaves like the oracle that knows the true model in advance, i.e. it is model selection consistent and estimates nonzero parameters with the standard rate. For the unweighted Lasso penalty, we obtain sufficient and necessary conditions for model selection consistency of estimators. The obtained results strongly based on the convexity of the loss function that is the main assumption of the paper. Our theorems can be applied to the ranking problem as well as generalised regression models. Thus, using U -statistics we can study more complex models (better describing real problems) than usually investigated linear or generalised linear models.