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Consistency of the GMLE with Mixed Case Interval‐Censored Data
Author(s) -
Schick Anton,
Yu Qiqing
Publication year - 2000
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00177
Subject(s) - mathematics , censoring (clinical trials) , consistency (knowledge bases) , weak consistency , interval (graph theory) , statistics , strong consistency , pointwise , pointwise convergence , network topology , discrete mathematics , combinatorics , estimator , mathematical analysis , computer science , operating system
In this paper we consider an interval censorship model in which the endpoints of the censoring intervals are determined by a two stage experiment. In the first stage the value k of a random integer is selected; in the second stage the endpoints are determined by a case k interval censorship model. We prove the strong consistency in the L 1 ( μ )‐topology of the non‐parametric maximum likelihood estimate of the underlying survival function for a measure μ which is derived from the distributions of the endpoints. This consistency result yields strong consistency for the topologies of weak convergence, pointwise convergence and uniform convergence under additional assumptions. These results improve and generalize existing ones in the literature.