廣義聯立方程模式與廣義路徑分析：存活或事件史資料(I)
Other Title
Is the Maximum Partial Likelihood Estimator for
Cox’s Proportional Hazards Model
Also a General Least Squares Estimator?
Cox’s Proportional Hazards Model
Also a General Least Squares Estimator?
Date Issued
2003-07-31
Date
2003-07-31
Author(s)
胡賦強
DOI
912118M002004
Abstract
The equivalences in estimation between the maximum likelihood approach (e.g., the
usual maximum likelihood estimator) and the least squares approach (e.g., the ordinary,
weighted, generalized, and iterative reweighted least squares estimators) have been estab-lished
for many well-known classes of statistical regression models such as linear regression
model, logistic regression model, and generalized linear models (GLMs). However, no such
connection has been discovered yet for the maximum partial likelihood estimator (MPLE) of
the regression coefficients in Cox’s proportional hazards model (Cox 1972, 1975). In this
study, by choosing an appropriate ”moment condition” of generalized method of moments
(GMM) estimation, we find that with the ”asymmetric orthogonal expected information ap-proach”
of adaptive estimation, the optimal martingale estimating function obtained from the
minimization of the corresponding GMM quadratic form for a consistent estimator of the
regression coefficients reduces to the partial score function of the Cox’s proportional hazards
model, which implies that the well-behaved MPLE is also a general least squares estimator.
This finding is not only very interesting in its own rights, but it provides us with an oppor-tunity
to develop GLMs-type regression models locally for stochastic processes and to apply
some powerful GMM-related estimating techniques such as the instrumental variables method
to deal with several known statistical modeling problems including measurement error and
simultaneous-equations bias in analysis of survival or time-to-event data.
Subjects
Partial score function
MPLE
Moment conditions
Generalized method of moments
GMM
Estimating functions
Martingales
Nuisance parameters
Adaptive estimation
Publisher
臺北市：國立臺灣大學公共衛生學院流行病學研究所
Type
report
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