On Minimum Distance Estimation for Binomial Regression Models

• Author / Creator

  Liu, Boxiao

• This thesis investigates efficient and robust estimators for binomial regression models. For this purpose, I have made use of two minimum distance estimation methods developed for discrete data, namely Minimum Hellinger Distance Estimation (MHDE) and Symmetric Chi-squared Distance Estimation (SCDE) methods. These methods generally known to produce efficient estimators when the chosen model is correct and, at the same time, are robust against model misspecification and outliers. Asymptotic properties and robustness features of the proposed estimators are discussed through theoretical demonstrations and simulations. Furthermore, the performance of estimators is compared with the traditional estimation approach of the maximum likelihood estimation. Binomial regression models generally requires a specified “link function.” In this thesis, cumulative distribution functions of the logistic and standard normal distributions are primarily used as the link functions. From theoretical results, it is concluded that the proposed MHDE is asymptotically equivalent to the maximum likelihood estimator when the model is correctly chosen. Some asymptotic properties of the proposed SCDE estimator is studied. Monte Carlo simulations are carried out compare the estimators for small to moderate sample sizes. It is observed that both MHDE and SCDE estimators show some robustness against model contamination, and the MHDE and the SCDE outperform the MLE in various conditions. Optimal conditions are discussed through extensive simulations under different scenarios.

• Subjects / Keywords

  • Binomial regression
  • Hellinger distance

• Graduation date

  Spring 2016

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3V40K692

• 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.