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

Stochastic Models in Probability and Statistics

مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 27 خرداد 1403   

نوع مقاله: Original Article

نویسنده

Isiaka Oloyede^*

Department of Statistics, University of Ilorin, Nigeria

چکیده

Regression is a generic tool used to make inferences in order to draw logical conclusions and judgement about a particular problem. It has been widely used in Engineering, Sciences, Education, Technology and social sciences over a long period of time. Breaking down of the underlying estimation mar the judgement and decision of the study, chiefly amongst 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 modelled with autocorrelated error whereas H_0 was modelled without, alternative approach in Bayes factor of AR(1) and MA(1) processes were introduced and compared it with Bayesian Information Criterion(BIC) approach in both negative and positive ρ(symettrical). The choice of the Bayes factor is due to the probabilistic nature of Bayesian inference which over the years has been performed better than the classical approach. The dataset with 5 covariates was 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 prior to estimation.

کلیدواژه‌ها

Bayes factor؛ Hypothesis؛ Restricted؛ Bayesian؛ Stein-Rule and Autocorrelated error