Jackknife Empirical Likelihood for the Variance in the Linear Regression Model

The variance of a random variable is σ. It is the measure of spread from the center. Therefore, how to accurately estimate variance (σ) has always been an important topic in recent years. In this paper, we consider a linear regression model which is the most popular model in practice. We use jackknife empirical likelihood (JEL) method to obtain the interval estimate of σ in the regression model. The proposed JEL ratio converges to the standard chi-squared distribution. The simulation study is carried out to compare the JEL, extended JEL, adjusted JEL methods and standard method in terms of coverage probability and interval length for the confidence intervals of σ from linear regression models. The proposed JEL, extended JEL and adjusted JEL has better performance than the standard method. We also illustrate the proposed methods using two real data sets. INDEX WORDS: Variance of error, Empirical likelihood, Jackknife empirical likelihood, Adjusted jackknife empirical likelihood, Extended jackknife empirical likelihood, Coverage probability, Interval length JACKKNIFE EMPIRICAL LIKELIHOOD FOR THE VARIANCE IN THE LINEAR REGRESSION MODEL