几乎无偏的回归估计器:波特兰水泥数据的理论比较与数值比较

IF 0.3 Q4 MATHEMATICS
S. Ng
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引用次数: 0

摘要

当自变量之间存在线性依赖关系时,就会出现多重共线性问题。当自变量之间存在相关性时,通常采用的普通最小二乘估计法(OLSE)并不适合线性回归模型。这是由于 OLSE 的方差较大,因此在存在多重共线性的情况下,OLSE 的准确性会降低。因此,本文提出了一种名为 K-almost unbiased regression estimator(KAURE)的估计器来替代 OLSE。KAURE 是通过使用几乎无偏估计器的定义来进一步减少刘式估计器特例(LTESC)的偏差而开发的。推导了 KAURE 的特性,包括偏差、方差-协方差和均方误差(MSE)。通过理论比较和实际数据比较,基于 MSE 标准评估了 KAURE 的性能。实际数据的应用支持了理论比较,表明 KAURE 优于 OLSE 和 LTESC。结果表明,KAURE 可被视为线性回归模型的替代估计器,以解决多重共线性问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An Almost Unbiased Regression Estimator: Theoretical Comparison and Numerical Comparison in Portland Cement Data
Multicollinearity is the problem when there is linear dependency among the independent variables. The Ordinary least squares estimator (OLSE) that is commonly adopted is not suitable for the linear regression model when the independent variables are correlated. This is due to the high variance in OLSE and hence the accuracy of OLSE reduces in the presence of multicollinearity. Hence, the estimator named k-almost unbiased regression estimator (KAURE) was proposed as an alternative to OLSE in this paper. KAURE was developed by using the definition of an almost unbiased estimator to further reduce the bias of Liu-type estimator-special case (LTESC). The properties of KAURE including bias, variance-covariance and mean squared error (MSE) were derived. Theoretical comparison and real-life data comparison were carried out to evaluate the performance of the KAURE based on the MSE criterion. The application of the real-life data supported the theoretical comparison that showed the superiority of KAURE over OLSE and LTESC. The results revealed that KAURE could be considered as an alternative estimator for the linear regression model to combat the problem of multicollinearity.
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来源期刊
Matematika
Matematika MATHEMATICS-
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