Séance Séminaire

Séminaire de Probabilités et Statistique

Estimation of functional sparsity in nonparametric varying coefficient models

Varying coefficient models are simple (concurrent) functional linear regression models for functional responses with many scalar or functional covariates. We study nonparametric estimation of coefficient functions for varying coefficient models in analysing longitudinal/functional data under a certain type of sparsity consideration. The problem of sparse estimation is well understood in the parametric setting as variable selection. Sparsity is the recurrent theme that could also encapsulate interpretability in the face of high dimensional regression. For nonparametric models, interpretability not only concerns the number of covariates involved but also the functional form of the estimates, and so the sparsity consideration is much more complex. To distinguish the types of sparsity in nonparametric models, we call the former global sparsity and the latter local sparsity, which constitute functional sparsity. Most existing methods focus on directly extending the framework of parametric sparsity for linear models to nonparametric function estimation to address one or the other, but not both. We develop a penalized estimation procedure that simultaneously addresses both types of sparsity in a unified framework. We establish asymptotic properties of estimation consistency and sparsistency of the proposed method. Our method is illustrated in simulation study and real data analysis, and is shown to outperform the existing methods in identifying both local sparsity and global sparsity. This is a joint work with Catherine Tu and Haonan Wang from Colorado State University