2001年6月
Kullback-Leibler information consistent estimation for censored data
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
- ,
- ,
- 巻
- 53
- 号
- 2
- 開始ページ
- 262
- 終了ページ
- 276
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- 出版者・発行元
- KLUWER ACADEMIC PUBL
This paper is intended as an investigation of parametric estimation for the randomly right censored data. In parametric estimation, the Kullback-Leibler information is used as a measure of the divergence of a true distribution generating a data relative to a distribution in an assumed parametric model M. When the data is uncensored, maximum likelihood estimator (MLE) is a consistent estimator of minimizing the Kullback-Leibler information, even if the assumed model M does not contain the true distribution. We call this property minimum Kullback-Leibler information consistency (MKLI-consistency). However, the MLE obtained by maximizing the likelihood function based on the censored data is not MKLI-consistent. As an alternative to the MLE, Oakes (1986, Biometrics, 42, 177-182) proposed an estimator termed approximate maximum likelihood estimator (AMLE) due to its computational advantage and potential for robustness. We show MKLI-consistency and asymptotic normality of the AMLE under the misspecification of the parametric model. In a simulation study, we investigate mean square errors of these two estimators and an estimator which is obtained by treating a jackknife corrected Kaplan-Meier integral as the log-likelihood. On the basis of the simulation results and the asymptotic results, we discuss comparison among these estimators. We also derive information criteria for the MLE and the AMLE under censorship, and which call be used not only for selecting models but also for selecting estimation procedures.
- リンク情報
- ID情報
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- ISSN : 0020-3157
- Web of Science ID : WOS:000169591400005