Hypothesis tests based on two-parameter biased estimators for significance of regression coefficients in case of multicollinearity

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Thesis Type: Postgraduate

Institution Of The Thesis: Gazi University, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2024

Thesis Language: Turkish

Student: Hilal KAPLAN TABAK

Supervisor: Meral Ebegil

Open Archive Collection: AVESIS Open Access Collection

Abstract:

In the linear regression model, multicollinearity problems arise when the assumption of no relationship between independent variables is not met. In this case, the estimations of the model parameters obtained by the Least Squares Estimator method deviate from the true value, leading to erroneous results. The Biased Estimator method is one of the effective methods used to eliminate the negative effects caused by multicollinearity. With this estimation method, it is aimed to reduce the increased variance and obtain consistent parameter estimates. The aim of this study is to obtain a test statistic for the Liu-Type Estimator to test the significance of the regression coefficients, using the test statistic obtained for the Ridge estimator in the study of Halawa and El-Bassiouni (2000). The significance tests of the regression model coefficients for the Ridge, Liu and Liu type biased estimators were conducted with a real data application and simulation study. The type-1 errors and power values of these estimators in different situations are calculated and the results obtained are compared. According to the results, when a high degree of multicollinearity is found, the LT1 test obtained for the Liu Type estimator is stronger than the other tests.

Key Words : Multicollinearity, biased estimators, hypothesis testing, type 1 error, powers of test