ABSTRACT
Examination and Comparison of the Performance of Common Non-Parametric and Robust Regression Models
By
Gregory Frank Malek
Stephen F. Austin State University, Masters in Statistics Program,
Nacogdoches, Texas, U.S.A.
This work investigated common alternatives to the least-squares regression method in the presence of non-normally distributed errors. An initial literature review identified a variety of alternative methods, including Theil Regression, Wilcoxon Regression, Iteratively Re-Weighted Least Squares, Bounded-Influence Regression, and Bootstrapping methods. These methods were evaluated using a simple simulated example data set, as well as various real data sets, including math proficiency data, Belgian telephone call data, and faculty salaries at the University of South Florida.
In addition, simulations were conducted of common error scenarios to test and evaluate each method. These simulations involved simple regression models in which the error terms were contaminated normal distributions with different amounts and magnitudes of contamination. The models were evaluated based on confidence interval coverage of regression coefficients, as well as bias and confidence interval width.
Finally, results were summarized, conclusions drawn, and suggestions for future applications of the results have been provided.
","abstract_html":"<p>ABSTRACT</p> <p>Examination and Comparison of the Performance of Common Non-Parametric and Robust Regression Models</p> <p>By</p> <p>Gregory Frank Malek</p> <p>Stephen F. Austin State University, Masters in Statistics Program,</p> <p>Nacogdoches, Texas, U.S.A.</p> <p><a href="mailto:g_m_2002@live.com">g_m_2002@live.com</a></p> <p>This work investigated common alternatives to the least-squares regression method in the presence of non-normally distributed errors. An initial literature review identified a variety of alternative methods, including Theil Regression, Wilcoxon Regression, Iteratively Re-Weighted Least Squares, Bounded-Influence Regression, and Bootstrapping methods. These methods were evaluated using a simple simulated example data set, as well as various real data sets, including math proficiency data, Belgian telephone call data, and faculty salaries at the University of South Florida.</p> <p>In addition, simulations were conducted of common error scenarios to test and evaluate each method. These simulations involved simple regression models in which the error terms were contaminated normal distributions with different amounts and magnitudes of contamination. The models were evaluated based on confidence interval coverage of regression coefficients, as well as bias and confidence interval width.</p> <p>Finally, results were summarized, conclusions drawn, and suggestions for future applications of the results have been provided.</p>","abstract_has_math":false,"creators":["Malek, Gregory F"],"institution":null,"degree_name":"Master of Science - Statistics","degree_level":"Thesis","degree_discipline":"Mathematics and Statistics","degree_department":null,"school":null,"contributors":["Dr. Robert K. Henderson"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-08-11T07:00:00Z","date_published":"2017-08-11T07:00:00Z","updated_at":"2026-07-24T04:30:15Z","subjects":["regression","robust","nonparametric","linear","simple linear model","Applied Statistics","Statistical Models","Statistical Theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.sfasu.edu/etds/120","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dr. Robert K. Henderson"]},{"key":"dc:creator","label":"Author","values":["Malek, Gregory F"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2017-08-11T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics and Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science - Statistics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["regression","robust","nonparametric","linear","simple linear model","Applied Statistics","Statistical Models","Statistical Theory"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.sfasu.edu/etds/120"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["ABSTRACT
Examination and Comparison of the Performance of Common Non-Parametric and Robust Regression Models
By
Gregory Frank Malek
Stephen F. Austin State University, Masters in Statistics Program,
Nacogdoches, Texas, U.S.A.
This work investigated common alternatives to the least-squares regression method in the presence of non-normally distributed errors. An initial literature review identified a variety of alternative methods, including Theil Regression, Wilcoxon Regression, Iteratively Re-Weighted Least Squares, Bounded-Influence Regression, and Bootstrapping methods. These methods were evaluated using a simple simulated example data set, as well as various real data sets, including math proficiency data, Belgian telephone call data, and faculty salaries at the University of South Florida.
In addition, simulations were conducted of common error scenarios to test and evaluate each method. These simulations involved simple regression models in which the error terms were contaminated normal distributions with different amounts and magnitudes of contamination. The models were evaluated based on confidence interval coverage of regression coefficients, as well as bias and confidence interval width.
Finally, results were summarized, conclusions drawn, and suggestions for future applications of the results have been provided.
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Examination and Comparison of the Performance of Common Non-Parametric and Robust Regression Models
By
Gregory Frank Malek
Stephen F. Austin State University, Masters in Statistics Program,
Nacogdoches, Texas, U.S.A.
This work investigated common alternatives to the least-squares regression method in the presence of non-normally distributed errors. An initial literature review identified a variety of alternative methods, including Theil Regression, Wilcoxon Regression, Iteratively Re-Weighted Least Squares, Bounded-Influence Regression, and Bootstrapping methods. These methods were evaluated using a simple simulated example data set, as well as various real data sets, including math proficiency data, Belgian telephone call data, and faculty salaries at the University of South Florida.
In addition, simulations were conducted of common error scenarios to test and evaluate each method. These simulations involved simple regression models in which the error terms were contaminated normal distributions with different amounts and magnitudes of contamination. The models were evaluated based on confidence interval coverage of regression coefficients, as well as bias and confidence interval width.
Finally, results were summarized, conclusions drawn, and suggestions for future applications of the results have been provided.
"],"dc:identifier":["https://scholarworks.sfasu.edu/etds/120"],"dc:subject":["regression","robust","nonparametric","linear","simple linear model","Applied Statistics","Statistical Models","Statistical Theory"],"dc:title":["Examination and Comparison of the Performance of Common Non-Parametric and Robust Regression Models"],"thesis:degree_discipline":["Mathematics and Statistics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science - Statistics"]},"updated_at":"2026-07-24T04:30:15Z"}