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

Yuan Wu, Ying Zhang

Research output: Contribution to journalArticle

4 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1609-1636
Number of pages28
JournalAnnals of Statistics
Volume40
Issue number3
DOIs
StatePublished - Jun 1 2012
Externally publishedYes

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Current Status Data
Cumulative distribution function
Joint Distribution
Spline
Monotone
Distribution Function
Tensor
Sieve
Maximum Likelihood Estimation
Constrained Estimation
Generalized Projection
Gradient Projection
B-spline Function
Generalized Gradient
Projection Algorithm
Gradient Algorithm
Constrained Optimization Problem
Regularity Conditions
Maximum Likelihood Estimator
Numerical Computation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Partially monotone tensor spline estimation of the joint distribution function with bivariate current status data. / Wu, Yuan; Zhang, Ying.

In: Annals of Statistics, Vol. 40, No. 3, 01.06.2012, p. 1609-1636.

Research output: Contribution to journalArticle

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