Partially monotone tensor spline estimation of the joint distribution function with bivariate current status data
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 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. © Institute of Mathematical Statistics,
2012.
Type
Journal articlePermalink
https://hdl.handle.net/10161/7384Published Version (Please cite this version)
10.1214/12-AOS1016Publication Info
Wu, Y; & Zhang, Y (2012). Partially monotone tensor spline estimation of the joint distribution function with
bivariate current status data. Annals of Statistics, 40(3). pp. 1609-1636. 10.1214/12-AOS1016. Retrieved from https://hdl.handle.net/10161/7384.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
Yuan Wu
Associate Professor in Biostatistics & Bioinformatics
Survival analysis, Sequential clinical trial design, Machine learning, Causal inference,
Non/Semi-parametric method, Statistical computing

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