針對半參數二元反應模型在補充性對照資料下之研究

Semiparametric Binary Response Models with Supplementary Case-Control Data

白任宏(Ren-Hong Bai)

指導教授 ： 江金倉

國立臺灣大學/理學院/數學研究所/碩士(2011年)

https://doi.org/10.6342/NTU.2011.01483

摘要

無資料

關鍵字

精確測度 ； 自助重取法 ； 交互驗證法 ； 虛擬最小平方估計法 ； 虛擬最大概似估計法 ； 單指標模型 ； 接受者操作特徵曲線 ； 補充性對照資料

並列摘要

The present study aimed to characterize the relationship between a binary response and covariates of interest through a more general single-index regression model. Based on case-control data supplemented by information on population totals, we primarily propose a pseudo likelihood estimation for the index coefficients of the considered semiparametric model. Two additional estimation procedures are further provided for different research purposes although the resulting estimators are relatively inefficient compared to the pseudo maximum likelihood one in general situations. Under the assumption of strictly increasing response function, an accuracy measure in the receiver operating characteristic curve analysis is borrowed to build an estimation criterion in which only those subjects with complete covariate information are included in estimation. To check the model correctness, a pseudo least squares estimation is employed as an aid to devising a suitable testing procedure. In addition, the general large sample properties of the proposed estimators and the related bootstrap inference procedures are developed. To assess the finite-sample performance of the estimation and inference procedures, an extensive simulation experiment is conducted. An empirical example from a lowbirthweight study in Auckland is also used to illustrate the applicability of our methodologies.

並列關鍵字

accuracy measure ； bootstrap ； cross-validation ； pseudo least squares estimator ； pseudo maximum likelihood estimator ； single-index model ； receiver operating characteristic curve ； supplementary case-control data.

參考文獻

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Bellman, R. (1961). Adaptive control processes: a guide tour. Princeton. New Jersey.

Breslow, N. E., McNeney, B., and Wellner, J. A. (2003). Large sample theory for semiparametric regression models with two-phase, outcome dependent sampling. Annals of Statistics. 31, 1110-1139.

Chiang, C. T. and Huang, M. Y. (2011). New estimation and inference procedures for a single-index conditional distribution model. Submitted.

Efron, B. (1979). Bootstrap methods: another look at the Jackknife. Annals of Statistics. 7, 1-26.