Robust Efficient Estimation of Semiparametric Covariate Models based on Minimum Hellinger Distance

Covariate models, such as polynomial regression models, generalized linear models, and heteroscedastic models, are widely used in statistical applications. The importance of such models in statistical analysis is abundantly clear by the ever-increasing rate at which articles on covariate models are appearing in the statistical literature. Because of their flexibility, covariate models are increasingly being exploited as a convenient way to model data that consist of both a response variable and one or more covariate variables that affect the outcome of the response variable. This thesis investigates efficient and robust estimates for this class of models. For this purpose, we employ the minimum distance approach which in general is automatically robust with respect to the stability of the quantity being estimated. In particular, the minimum Hellinger distance estimation (MHDE) introduced by Beran (1977) for parametric models produces estimators that are asymptotically efficient at the model density and simultaneously possess excellent robustness properties. Wu and Karunamuni (2015) extended the idea and proposed the minimum profile Hellinger distance estimation (MPHDE) for semiparametric models of general form. In this thesis, we first construct an MPHDE for single-index models which are the most commonly used covariate models, prove its consistency, and examine its finite-sample performance and robustness properties via Monte Carlo simulation studies and real data analysis. We further extend the MPHDE to the general covariate models, in which we prove the consistency and asymptotic normality of the proposed MPHDE and a computing algorithm is developed to ease the computation of the estimate. Its finite-sample performance, including efficiency and robustness, are examined by simulation studies and real data applications.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Discipline thesis:degree_discipline

Mathematics & Statistics

Grantor

Science

Year dc:date.issued

2025

Author dc:creator

• Ding, Bowei

Advisor dc:contributor.advisor

• Wu, Jingjing

Committee members dc:contributor.committeemember

• Lu, Xuewen
• de Leon, Alexander

Statement dc:rights

• Unless otherwise indicated, this material is protected by copyright and has been made available with authorization from the copyright owner. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.

Language dc:language.iso

en

DOI

https://dx.doi.org/10.11575/PRISM/50178

OAI identifier oai:identifier

oai:ucalgary.scholaris.ca:1880/122585