Bayes factor: hypothesis testing in restricted Stein-rule regression analysis with autocorrelated error

Document Type : Original Article

Author

• Isiaka Oloyede

Department of Statistics, University of Ilorin, Nigeria

10.22067/smps.2024.45179

Abstract

Regression is a generic tool used to make inferences so as to draw logical conclusions and judgments about a particular problem. It has been widely used in engineering, sciences, education, technology, and social sciences for a long time. Breaking down of the underlying estimation mar the judgment and decision of the study. Chiefly among the error structure that can lead to the drawback of the inferences of regression is the autocorrelation of error term of both AR and MA processes. Restricted Stein-rule regression analysis was used with data injected with autocorrelated error; H_1 was modeled with autocorrelated error whereas H_0 was modeled without, alternative approach in Bayes factor of AR(1) and MA(1) processes were introduced and compared  with Bayesian information criterion  approach in both negative and positive rho  (symmetrical). The choice of the Bayes factor (Bf) is due to the probabilistic nature of Bayesian inference, which over the years has been performed better than the classical approach. The datasets with five covariates were set at 25 to capture the error structure and project the property of a small sample. The study, therefore, concluded that Bayesian inference being probabilistic about the uncertainty of the parameters should be adopted to verify the presence or absence of autocorrelated error in the data before estimation.

Keywords

• Autocorrelated Error
• Bayesian
• Bayes factor
• Hypothesis
• Restricted
• Stein-Rule

---