A penalized estimation procedure for varying coefficient models

Varying coefficient models are widely used for analyzing longitudinal data. Various methods for estimating coefficient functions have been developed over the years. We revisit the problem under the theme of functional sparsity. The problem of sparsity, including global sparsity and local sparsity, is a recurrent topic in nonparametric function estimation. A function has global sparsity if it is zero over the entire domain, and it indicates that the corresponding covariate is irrelevant to the response variable. A function has local sparsity if it is nonzero but remains zero for a set of intervals, and it identifies an inactive period of the corresponding covariate. Each type of sparsity has been addressed in the literature using the idea of regularization to improve estimation as well as interpretability. In this dissertation, a penalized estimation procedure has been developed to achieve functional sparsity, that is, simultaneously addressing both types of sparsity in a unified framework. We exploit the property of B-spline approximation and group bridge penalization. Our method is illustrated in simulation study and real data analysis, and outperforms the existing methods in identifying both local sparsity and global sparsity. Asymptotic properties of estimation consistency and sparsistency of the proposed method are established. The term of sparsistency refers to the property that the functional sparsity can be consistently detected.

Name thesis:degree_name

Doctor of Philosophy (Ph.D.)

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Statistics

Grantor dc:publisher

Colorado State University. Libraries

Year dc:date.issued

2015

Authors dc:creator

• Tu, Yan, author
• Wang, Haonan, advisor
• Breidt, F. Jay, committee member
• Chapman, Phillip, committee member
• Luo, J. Rockey, committee member

Statement dc:rights

• Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.

Language dc:language.iso

eng, English

Identifier URI

https://doi.org/10.25675/3.018733

OAI identifier oai:identifier

oai:mountainscholar.org:10217/170359