胡賦強2006-07-252018-06-292006-07-252018-06-292003-07-31http://ntur.lib.ntu.edu.tw//handle/246246/4688The 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.application/pdf371066 bytesapplication/pdfzh-TW國立臺灣大學公共衛生學院流行病學研究所Partial score functionMPLEMoment conditionsGeneralized method of momentsGMMEstimating functionsMartingalesNuisance parametersAdaptive estimationreporthttp://ntur.lib.ntu.edu.tw/bitstream/246246/4688/1/912118M002004.pdf