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Theory & Methods: Semi‐parametric modelling and likelihood estimation with estimating equations
Author(s) -
Lu JyeChyi,
Chen Di,
Gan Nianci
Publication year - 2002
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00222
Subject(s) - mathematics , estimating equations , parametric statistics , likelihood function , empirical likelihood , statistics , parametric model , restricted maximum likelihood , semiparametric model , sample size determination , regression analysis , maximum likelihood , estimation theory , econometrics , confidence interval
This paper proposes a semi‐parametric modelling and estimating method for analysing censored survival data. The proposed method uses the empirical likelihood function to describe the information in data, and formulates estimating equations to incorporate knowledge of the underlying distribution and regression structure. The method is more flexible than the traditional methods such as the parametric maximum likelihood estimation (MLE), Cox’s (1972) proportional hazards model, accelerated life test model, quasi‐likelihood (Wedderburn, 1974) and generalized estimating equations (Liang & Zeger, 1986). This paper shows the existence and uniqueness of the proposed semi‐parametric maximum likelihood estimates (SMLE) with estimating equations. The method is validated with known cases studied in the literature. Several finite sample simulation and large sample efficiency studies indicate that when the sample size is larger than 100 the SMLE is compatible with the parametric MLE; and in all case studies, the SMLE is about 15% better than the parametric MLE with a mis‐specified underlying distribution.