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Maximum Likelihood Estimation in a Semiparametric Logistic/Proportional‐Hazards Mixture Model
Author(s) -
FANG HONGBIN,
LI GANG,
SUN JIANGUO
Publication year - 2005
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/j.1467-9469.2005.00415.x
Subject(s) - mathematics , statistics , semiparametric model , estimation , maximum likelihood , logistic regression , econometrics , parametric statistics , management , economics
. We consider large sample inference in a semiparametric logistic/proportional‐hazards mixture model. This model has been proposed to model survival data where there exists a positive portion of subjects in the population who are not susceptible to the event under consideration. Previous studies of the logistic/proportional‐hazards mixture model have focused on developing point estimation procedures for the unknown parameters. This paper studies large sample inferences based on the semiparametric maximum likelihood estimator. Specifically, we establish existence, consistency and asymptotic normality results for the semiparametric maximum likelihood estimator. We also derive consistent variance estimates for both the parametric and non‐parametric components. The results provide a theoretical foundation for making large sample inference under the logistic/proportional‐hazards mixture model.