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Goodness‐of‐fit Tests for Semi‐Markov and Markov Survival Models with One Intermediate State
Author(s) -
Chang IShou,
Chuang YuanChuan,
Hsiung Chao A.
Publication year - 2001
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 - 10.1111/1467-9469.00251
Subject(s) - mathematics , goodness of fit , statistics , markov chain , estimator , consistency (knowledge bases) , counting process , markov model , weak convergence , discrete mathematics , computer science , computer security , asset (computer security)
Survival data with one intermediate state are described by semi‐Markov and Markov models for counting processes whose intensities are defined in terms of two stopping times T 1 < T 2 . Problems of goodness‐of‐fit for these models are studied. The test statistics are proposed by comparing Nelson–Aalen estimators for data stratified according to T 1 . Asymptotic distributions of these statistics are established in terms of the weak convergence of some random fields. Asymptotic consistency of these test statistics is also established. Simulation studies are included to indicate their numerical performance.