  The analysis of the joint cumulative distribution function (CDF) 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 CDF with bivariate current status data.
The I-splines are used to approximate the joint CDF in order to simplify the
numerical computation of a constrained maximum likelihood estimation problem.
The generalized gradient projection algorithm is used to compute the
constrained optimization problem. Based on the properties of B-spline basis
functions it is shown that the proposed tensor spline-based nonparametric sieve
maximum likelihood estimator is consistent with a rate of convergence
potentially better than $n^{1/3}$ under some mild 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.
