The partially monotone tensor spline estimation of joint distribution function with bivariate current status data

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.