Off-campus UMass Amherst users: To download campus access dissertations, please use the following link to log into our proxy server with your UMass Amherst user name and password.
Non-UMass Amherst users: Please talk to your librarian about requesting this dissertation through interlibrary loan.
Dissertations that have an embargo placed on them will not be available to anyone until the embargo expires.
Author ORCID Identifier
https://orcid.org/0000-0003-3761-7904
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
Year Degree Awarded
2019
Month Degree Awarded
September
First Advisor
Anna Liu
Subject Categories
Statistical Methodology | Statistical Theory
Abstract
We study the joint asymptotics of general smoothing spline semiparametric models in the settings of density estimation and regression. We provide a systematic framework which incorporates many existing models as special cases, and further allows for nonlinear relationships between the finite-dimensional Euclidean parameter and the infinite-dimensional functional parameter. For both density estimation and regression, we establish the local existence and uniqueness of the penalized likelihood estimators for our proposed models. In the density estimation setting, we prove joint consistency and obtain the rates of convergence of the joint estimator in an appropriate norm. The convergence rate of the parametric component in the standard Euclidean norm and the convergence for the overall density function in the symmetric Kullback-Leibler (SKL) metric are also established. Finally, for our regression model, we obtain the joint consistency and rates of convergence in parallel to those for the density estimation model. In addition, we investigate a doubly penalized likelihood estimator in terms of joint consistency, parameter estimation consistency, and model selection consistency.
DOI
https://doi.org/10.7275/15233553
Recommended Citation
Yu, Jiahui, "Joint Asymptotics for Smoothing Spline Semiparametric Nonlinear Models" (2019). Doctoral Dissertations. 1786.
https://doi.org/10.7275/15233553
https://scholarworks.umass.edu/dissertations_2/1786