Abstract

In classical linear regression analysis problems, the ordinary least-squares (OLS) estimation is the popular method to obtain the regression weights, given the essential assumptions are satisfied. However, often, in real-life studies, the response data and its associated explanatory variables do not meet the required conditions, in particular under multicollinearity, and hence results can be misleading. To overcome such problem, this paper introduces a novel generalized difference-based weighted mixed almost unbiased Liu estimator. The performance of this new estimator is evaluated against the classical estimators using the mean squared error. This is followed by an approach to select the Liu parameter and in this context, a non-stochastic weight is also considered. Monte Carlo simulation experiments are executed to assess the performance of the new estimator and subsequently,we illustrate its application to a real-life data example.

摘要

在经典线性回归分析问题中，在满足基本假设的情况下，普通最小二乘 (OLS) 估计是获得回归权重的常用方法。然而，在现实生活中的研究中，响应数据及其相关的解释变量通常不符合要求的条件，特别是在多重共线性的情况下，因此结果可能会产生误导。为了克服这个问题，本文介绍了一种新颖的基于广义差异的加权混合几乎无偏的刘估计量。使用均方误差针对经典估计器评估此新估计器的性能。随后是一种选择 Liu 参数的方法，在这种情况下，还考虑了非随机权重。