Partially monotone tensor spline estimation of the joint distribution function with bivariate current status data
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.
Published Version (Please cite this version)10.1214/12-AOS1016
Publication InfoWu, 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 http://hdl.handle.net/10161/7384.
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