Document Type
Dissertation
Date of Degree
Summer 2010
Degree Name
PhD (Doctor of Philosophy)
Degree In
Applied Mathematical and Computational Sciences
First Advisor
Ying Zhang
First Committee Member
Ying Zhang
Second Committee Member
Weimin Han
Third Committee Member
Jian Huang
Fourth Committee Member
Michael Jones
Fifth Committee Member
Lihe Wang
Abstract
The analysis of joint distribution function with bivariate event time data is a challenging problem both theoretically and numerically. This thesis develops a tensor splinebased nonparametric maximum likelihood estimation method to estimate the joint distribution function with bivariate current status data.
The tensor I-splines are developed to replace the traditional tensor B-splines in approximating joint distribution function in order to simplify the restricted maximum likelihood estimation problem in computing. The generalized gradient projection algorithm is used
to compute the restricted optimization problem. We show that the proposed tensor spline-based nonparametric estimator is consistent and that the rate of convergence is obtained. Simulation studies with moderate sample sizes show that the finite-sample performance of the proposed estimator is generally satisfactory.
Pages
xi, 128 pages
Bibliography
Includes bibliographical references (pages 124-126).
Copyright
Copyright 2010 Yuan Wu