Penalized Spline Estimation in the Partially Linear Model

Author

Ashley D. Holland, Cedarville UniversityFollow

Date of Award

2012

Document Type

Dissertation

Degree Name

Doctor of Philosophy (Ph.D.)

Institution Granting Degree

University of Michigan

Cedarville University School or Department

Science and Mathematics

First Advisor

Matias Cattaneo

Second Advisor

Virginia Young

Keywords

Social sciences, applied sciences, penalized spline estimation, series estimation, asymptotic normality, regression splines, smoothing splines, rates of convergence, semi linear models

Abstract

Penalized spline estimators have received considerable attention in recent years because of their good finite-sample performance, especially when the dimension of the regressors is large. In this project, we employ penalized B-splines in the context of the partially linear model to estimate the nonparametric component, when both thenumber of knots and the penalty factor vary with the sample size. We obtain mean-square convergence rates and establish asymptotic distributional approximations, with valid standard errors, for the resulting multivariate estimators of both the parametric and nonparametric components in this model. Our results extend and complement the recent theoretical work in the literature on penalized spline estimators by allowing for multivariate covariates, heteroskedasticity of unknown form, derivative estimation, and statistical inference in the semi-linear model, using weaker assumptions. The results from a simulation study are also reported.

Comments

© 2012 Ashley D. Holland. All rights reserved.

Recommended Citation

Holland, Ashley D., "Penalized Spline Estimation in the Partially Linear Model" (2012). Faculty Dissertations. 33.
https://digitalcommons.cedarville.edu/faculty_dissertations/33