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Robust Adaptively Weighted Estimators for Regression Models Open Access


Other title
weighted estimators
robust statistics
regression model
adaptive estimators
Type of item
Degree grantor
University of Alberta
Author or creator
Tu, Wei
Supervisor and department
Rohana, Karunamuni (Mathematical and Statistical Sciences)
Examining committee member and department
Rohana, Karunamuni (Mathematical and Statistical Sciences)
Irina, Dinu (Public Health)
Linglong, Kong (Mathematical and Statistical Sciences)
Bei, Jiang (Mathematical and Statistical Sciences)
Department of Mathematical and Statistical Sciences
Date accepted
Graduation date
Master of Science
Degree level
This thesis introduces a new class of robust estimators for regression mod- els. Specifically, a class of weighted least square estimators under linear re- gression models is introduced in Chapter 2, with a continuous adaptive weight function computed using the Kolmogorov-Smirnov statistic. Asymptotic prop- erties, such as consistency and asymptotic normality, of the proposed estimator are established under the model. Simulation studies show that the proposed estimator attains almost full e�ciency and have a better robustness proper- ties than the initial estimators for finite sample sizes. An application to a real contaminated dataset shows that it’s comparable to other robust estimators in practice. In Chapter 3, a class of weighted maximum likelihood estimators under logistic regression models is introduced, again with a continuous adaptive weight function computed using Mahalanobis distances of exploratory vari- ables. Asymptotic consistency of the proposed estimator is proved under the model, and finite-sample properties are also studied by simulation. In simu- lation studies, it is observed that the proposed estimator is almost as e�cient as the maximum likelihood estimator under the model, and under point-mass contamination models, the proposed estimator shows a comparable robustness. This is also verified in an application to a real data set. Chapter 4 contains some concluding remarks and future directions.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
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