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oai:mountainscholar.org:10217/1703592025-12-30T03:30:42Zcom_10217_100532com_10217_100000com_10217_100518com_10217_100303col_10217_100538col_10217_100519

Tu, Yan, author Wang, Haonan, advisor Breidt, F. Jay, committee member Chapman, Phillip, committee member Luo, J. Rockey, committee member 2016-01-11T15:13:52Z 2016-01-11T15:13:52Z 2015 Tu_colostate_0053A_13332.pdf http://hdl.handle.net/10217/170359 https://doi.org/10.25675/3.018733 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. born digital doctoral dissertations English eng Colorado State University. Libraries 2000-2019 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. A penalized estimation procedure for varying coefficient models Text Doctor of Philosophy (Ph.D.) Doctoral Statistics Colorado State University This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). open.access