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Robust Adaptively Weighted Estimators for Regression Models

  • Author / Creator
    Tu, Wei
  • 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.

  • Subjects / Keywords
  • Graduation date
    2015-11
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3X921V92
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Statistics
  • Supervisor / co-supervisor and their department(s)
    • Rohana, Karunamuni (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Bei, Jiang (Mathematical and Statistical Sciences)
    • Rohana, Karunamuni (Mathematical and Statistical Sciences)
    • Irina, Dinu (Public Health)
    • Linglong, Kong (Mathematical and Statistical Sciences)