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008 120107s2010 ||||||||||||||||| ||eng d

020 $a9780494649008

035 $a00218573

090 $aE-BOOK/378.242/York/2010///UM043267

100 1 $aGuo, Pengfei.$3326102

245 10$aRobust inference and weighted likelihood estimation$h[electronic resource] /$cPengfei Guo.

260 $aAnn Arbor :$bProQuest Dissertations & Theses,$c2010.

300 $a106 p.

500 $aSource: Dissertation Abstracts International, Volume: 71-09, Section: B, page: 5507.

502 $aThesis (Ph.D.)--York University (Canada), 2010.

520 $aHu and Zidek (1997) proposed a very general method for using all relevant information in statistical inference. We extend their method to generalized linear models when the covariates are generated from different populations. Furthermore, we propose a unified and effective method to choose the weights using the estimated probability of membership through the expectation-maximization algorithm when memberships are unknown. The proposed weights are applicable to both discrete and continuous covariates and work well in generalized linear models. We also derive the asymptotic properties of the estimator based on the weighted likelihood equations.

520 $aNotice that the method we proposed above only control the model uncertainty on the covariates directions, in the second part of the thesis, we employ robust techniques, such as M-estimation, to control the possible model violation on the response direction. M-estimator is a broad class of estimators which are obtained by minimizing certain functions of the data which have robust properties.

520 $aSimulation studies are provided to demonstrate the performance of the new methods. Examples of the real data analysis are also presented. Our simulation studies suggested that the weighted likelihood with the proposed weights is more powerful in testing than the classical MLE. The weighted M-estimator is not only efficient in estimating the parameters in the main cluster, but also robust to influential points. Applications to real data sets imply that our method can detect real relationships that the classical method failed to discover.

520 $aIn the end of the thesis, we also consider the weighted likelihood when the memberships of observations are known.

590 $aSchool code: 0267.

650 4$aMathematics.$3148222

710 2 $aYork University (Canada).$3238440

773 0 $tDissertation Abstracts International$g71-09B.

791 $aPh.D.

792 $a2010

856 40$uhttps://erm.library.ntpu.edu.tw/login?url=http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=NR64900$z線上閱讀(PQDT論文)

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