Abstract

Variance estimation is fundamental in the statistical inference. Due to the nonlinearity of the variance estimator, Lin et al. [Jackknife empirical likelihood for the error variance in linear models. J Nonparametr Stat. 2017;29:151–166.] proposed the jackknife empirical likelihood method for the error variance in a linear regression model. However, people may have some prior information about the error variance. In this article, we propose the Bayesian jackknife empirical likelihood (BJEL) for the error variance in a linear regression model. The validity of the proposed method is verified, and the asymptotic normal properties for the BJEL are also established. A simulation study shows that the new approach for the small sample performs better than its frequentist counterpart. Two real data sets are also used to illustrate the proposed methods.

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