Partially Monotone Tensor Spline Estimation of the Joint Distribution Function with Bivariate Current Status Data

The analysis of the joint distribution function with bivariate event time data is a challenging problem both theoretically and numerically. This paper develops a tensor spline-based sieve maximum likelihood estimation method to estimate the joint distribution function with bivariate current status data. The I-spline basis functions are used in approximating the joint distribution function in order to simplify the numerical computation of constrained maximum likelihood estimation problem. The generalized gradient projection algorithm is used to compute the constrained optimization problem. The proposed tensor spline-based nonparametric sieve maximum likelihood estimator is shown to be consistent and the rate of convergence can be as good as n 1/4 under some 1 regularity conditions. The simulation studies with moderate sample sizes are carried out to demonstrate that the finite sample performance of the proposed estimator is generally satisfactory.