Generalized MLE of a joint distribution function with multivariate interval-censored data
We consider the estimation of a joint distribution function \(F_0\) of a multivariate random vector \({\mathbf X}=(X_1, \dots, X_d)\) which is subject to interval censoring. In interval censoring, the value of each coordinate variable \(X_i\) may not be directly observable; instead, a pair of extended real numbers \(L_i\) and \(R_i\) such that \(L_i\leq X_i\leq R_i\) are always observed. The observations \(L_i\) and \(R_i\) satisfy one of the following four conditions: \(L_i=R_i\) (exact), \(0=L_i<R_i\) (left censored), \(L_i<R_i =\infty\) (right censored), and \(0<L_i<R_i <\infty\) (strictly interval censored). A \(d\)-dimensional interval-censored observation corresponding to \({\mathbf X}\) is represented by the \(2d\)-dimensional vector \((L_1,R_1, \dots, L_d,R_d)\). In Section 2, we discuss generalized maximum likelihood estimation of \(F_0\) based on multivariate interval-censored data and formulate the case 2 multivariate interval censorship model. We establish consistency of the generalized maximum likelihood estimate (GMLE) of \(F_0\) in Section 3 and asymptotic normality of the GMLE in Section 4.
scientific article; zbMATH DE number 1310062
scientific article