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Estimation of a Joint Distribution Function with Multivariate Interval‐Censored Data when the Nonparametric MLE is not Unique
Author(s) -
Yu Qiqing,
Wong George Y.C.,
He Qimei
Publication year - 2000
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/1521-4036(200010)42:6<747::aid-bimj747>3.0.co;2-w
Subject(s) - mathematics , statistics , estimator , nonparametric statistics , multivariate statistics , survival function , univariate , multivariate normal distribution , matrix t distribution , estimation of covariance matrices
A nonparametric estimator of a joint distribution function F 0 of a d‐dimensional random vector with interval‐censored (IC) data is the generalized maximum likelihood estimator (GMLE), where d ≥ 2. The GMLE of F 0 with univariate IC data is uniquely defined at each follow‐up time. However, this is no longer true in general with multivariate IC data as demonstrated by a data set from an eye study. How to estimate the survival function and the covariance matrix of the estimator in such a case is a new practical issue in analyzing IC data. We propose a procedure in such a situation and apply it to the data set from the eye study. Our method always results in a GMLE with a nonsingular sample information matrix. We also give a theoretical justification for such a procedure. Extension of our procedure to Cox's regression model is also mentioned.