Research Information System
Thesis Type: Postgraduate
Institution Of The Thesis: Gazi University, Fen Bilimleri Enstitüsü, Turkey
Approval Date: 2023
Thesis Language: Turkish
Student: Gizem İklil KOCASOY
Supervisor: Meral Ebegil
Open Archive Collection: AVESIS Open Access Collection
Abstract:
One of the most fundamental problems in multiple linear regression analysis is the multicollinearity problem. In the case of multicollinearity in the model, the Ordinary Least Squares estimator is unbiased, but its variance is overgrown. Therefore, the parameter estimation value obtained from the Ordinary Least Squares estimator deviates from the actual value of the parameter. Using biased estimators to eliminate the problem of multicollinearity has been proposed as a solution. The Ridge Regression estimator is frequently preferred among these biased estimators. The Liu estimator was proposed as an alternative to the Ridge estimator. In this study, the Simulated Annealing algorithm, which performed better for certain conditions than the previously proposed Particle Swarm Optimization method, was proposed to find the optimal bias parameter for Ridge and Liu regression estimators. The bias parameters proposed with Particle Swarm Optimization and Simulated Annealing algorithms were compared with the bias parameters previously proposed by different researchers in the literature in terms of the Mean Square Error criteria with a simulation study by using different correlations, different variance values, different explanatory variable numbers, and different sample sizes. In this study Particle Swarm Optimization and Simulated Annealing optimization methods perform better than the classical methods proposed in the literature. In addition, when the Simulated Annealing Optimization algorithm and the Particle Swarm Optimization algorithm are compared among themselves, for the Liu estimator the Simulated Annealing Optimization algorithm and for Ridge estimator Particle Swarm Optimization gives better results in terms of the Mean Squared Error criterion. This study was supported by an application based on real-life data and as a result of the application, it was shown that Simulated Annealing algorithm gives better performance according to the Variance Inflation Factor criteria.
Key Words : Multicollinearity, biased estimation methods, ridge, liu, particle
swarm optimization, simulated annealing optimization