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Permanent link (DOI): https://doi.org/10.7939/R3V40K692

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On Minimum Distance Estimation for Binomial Regression Models Open Access

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Other title
Subject/Keyword
binomial regression
Hellinger distance
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Liu, Boxiao
Supervisor and department
Karunamuni, Rohana
Examining committee member and department
Jiang, Bei (Statistics)
Karunamuni, Rohana (Statistics)
Wang, Yau shu (Mathematics)
Kong, Linglong (Statistics)
Department
Department of Mathematical and Statistical Sciences
Specialization
Statistics
Date accepted
2016-01-18T16:08:28Z
Graduation date
2016-06
Degree
Master of Science
Degree level
Master's
Abstract
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.
Language
English
DOI
doi:10.7939/R3V40K692
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. 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.
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