Term of Award

Summer 2024

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Copyright Statement / License for Reuse

Digital Commons@Georgia Southern License

Department

Department of Mathematical Sciences

Committee Chair

Divine Wanduku

Committee Member 1

Charles Champ

Committee Member 2

Stephen Carden

Committee Member 3

Andrew Sills

Committee Member 3 Email

asills@georgiasouthern.edu

Abstract

Classical statistical supervised learning optimization techniques like the Gauss-Newton Iterative Method (GNIM), Weighted Gauss-Newton Iterative Method (WGNIM), Reweighted Gauss-Newton Iterative Method (RGNIM), and Levenberg-Marquart (LM) algorithm extend the nonlinear least squares method. The WGNIM improves model fitting by controlling heteroscedasticity in the linear and nonlinear models. A comparative analysis of the GNIM, WGNIM, RGNIM, and LM methods for fitting nonlinear models is presented. A step-wise diagnosis for structural multicollinearity in the reweighted linearized model is investigated via the Variance Inflation Factor (VIF) to determine variance inflation in the sequence of estimators for the model parameters. Under restricted multicollinearity levels in simulated experiments, the RGNIM outperforms the GNIM with respect to precision, while the LM is most flexible for selecting the initial parameter estimate among all of the algorithms. Meanwhile, RGNIM and WGNIM have longer computational times.

Research Data and Supplementary Material

No

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