Partially monotone tensor spline estimation of the joint distribution function with bivariate current status data

TL;DR

This paper introduces a tensor spline-based nonparametric estimator for the joint distribution function using bivariate current status data, demonstrating its consistency and good finite sample performance.

Contribution

It develops a novel tensor spline sieve maximum likelihood method for estimating the joint CDF with bivariate current status data, improving computational feasibility and theoretical properties.

Findings

Estimator is consistent with a convergence rate potentially better than n^{1/3}

Simulation studies show satisfactory finite sample performance

Method simplifies numerical computation of constrained MLE for joint CDF

Abstract

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.