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arXiv · 1209.5543

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

Yuan Wu·Ying Zhang
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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.

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Yuan Wu, Ying Zhang. 2012-09-25. Partially monotone tensor spline estimation of the joint distribution function with bivariate current status data. https://doi.org/10.1214/12-aos1016

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