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Statistica Sinica 25 (2015), 1337-1354

FUNCTIONAL SPARSITY: GLOBAL VERSUS LOCAL
Haonan Wang and Bo Kai
Colorado State University and College of Charleston

Abstract: We consider the model selection problem in nonparametric regression. The notion of functional sparsity is a generalization of parameter sparsity in parametric models. In particular, two types of sparsity are studied, global and local sparsity. The goal is to produce a sparse estimate, that assigns zero values over regions where the true underlying function is zero. Most classical smoothing techniques yield consistent estimates with no sparsity. Here, a penalized least squares procedure, based on a basis function approximation and the group bridge penalty function, is proposed for simultaneous function estimation and zero subregion detection. Asymptotic properties, including both consistency in estimation and sparsistency in model selection, of the procedure are established. The methodology is illustrated through simulation studies and a case study.

Key words and phrases: Functional data analysis, group bridge, model selection, smoothing.

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