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

• 成果类型: Article
• 署名作者: Wu, Yuan; Zhang, Ying
• 署名单位: University of California System; University of California San Diego; University of Iowa
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1016
• 发表日期: 2012
• 页码: 1609-1636
• 关键词: maximum-likelihood-estimation; interval-censored-data; failure time data; efficient estimation; statistical-analysis; regression-analysis; polynomial splines; DENSITY-ESTIMATION; MODEL; association

摘要

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.