Journal Article

PARTIALLY MONOTONE TENSOR SPLINE ESTIMATION OF THE JOINT DISTRIBUTION FUNCTION WITH BIVARIATE CURRENT STATUS DATA

Zhang, Ying, Wu, Yuan

2012

Overview

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 n¹ / 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.

• Publisher: Institute of Mathematical Statistics,The Institute of Mathematical Statistics
• Subject: 60F05 / 60F17 / 60G05 / Bivariate current status data / Censored data / constrained maximum likelihood estimation / Cumulative distribution functions / empirical process / Estimates / Estimation bias / Estimation methods / Estimators / Maximum likelihood estimation / Maximum likelihood estimators / Optimization / Probability distribution / Sample size / Sampling bias / sieve maximum likelihood estimation / Simulation / Studies / tensor spline basis functions / Tensors