Nonparametric Bayesian estimation of a survival curve with dependent censoring mechanism
Let \((X_ 1,Y_ 1),...,(X_ N,Y_ N)\) be a random sample from a bivariate distribution function F corresponding to a Dirichlet process on \({\mathbb{R}}_+^ 2\). Under the squared error loss function the Bayes estimator of F is obtained, which is based on observing only \((\delta_ i,\min (X_ i,Y_ i))\), where \(\delta_ i=1\) if \(X_ i\leq Y_ i\) and \(=0\) otherwise, \(i=1,2,...,n.\) It should be pointed out that \(X_ i\) and \(Y_ i\) need not be independent which is the usual assumption in survival analysis models. An example of the estimator is given when Freunds' bivariate exponential is assumed as the parameter of the Dirichlet process. Numerical comparison of this estimator and some other estimators in the independent case is also presented.
scientific article; zbMATH DE number 3913459