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June 2012 Partially monotone tensor spline estimation of the joint distribution function with bivariate current status data
Yuan Wu, Ying Zhang
Ann. Statist. 40(3): 1609-1636 (June 2012). DOI: 10.1214/12-AOS1016

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.

Citation

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Yuan Wu. Ying Zhang. "Partially monotone tensor spline estimation of the joint distribution function with bivariate current status data." Ann. Statist. 40 (3) 1609 - 1636, June 2012. https://doi.org/10.1214/12-AOS1016

Information

Published: June 2012
First available in Project Euclid: 5 September 2012

zbMATH: 1254.62046
MathSciNet: MR3015037
Digital Object Identifier: 10.1214/12-AOS1016

Subjects:
Primary: 60F05, 60F17
Secondary: 60G05

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 3 • June 2012
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