Linear regression models are useful statistical tools to analyze data sets in different fields. There are several methods to estimate the parameters of a linear regression model. These methods usually perform under normally distributed and uncorrelated errors. If error terms are correlated the Conditional Maximum Likelihood (CML) estimation method under normality assumption is often used to estimate the parameters of interest. The CML estimation method is required a distributional assumption on error terms. However, in practice, such distributional assumptions on error terms may not be plausible. In this paper, we propose to estimate the parameters of a linear regression model with autoregressive error term using Empirical Likelihood (EL) method, which is a distribution free estimation method. A small simulation study is provided to evaluate the performance of the proposed estimation method over the CML method. The results of the simulation study show that the proposed estimators based on EL method are remarkably better than the estimators obtained from CML method in terms of mean squared errors (MSE) and bias in almost all the simulation configurations. These findings are also confirmed by the results of the numerical and real data examples.

线性回归模型是分析不同领域数据集的有用统计工具。有几种方法可以估计线性回归模型的参数。这些方法通常在正态分布且不相关的误差下执行。如果误差项相关，则通常使用正态假设下的条件最大似然 (CML) 估计方法来估计感兴趣的参数。CML 估计方法需要对误差项进行分布假设。然而，在实践中，这种关于误差项的分布假设可能并不合理。在本文中，我们建议使用经验似然（EL）方法估计具有自回归误差项的线性回归模型的参数，这是一种无分布估计方法。提供了一个小型模拟研究来评估所提出的估计方法相对于 CML 方法的性能。仿真研究结果表明，在几乎所有仿真配置中，基于 EL 方法的估计量在均方误差 (MSE) 和偏差方面都明显优于从 CML 方法获得的估计量。数值和真实数据示例的结果也证实了这些发现。