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An effective approach towards efficient estimation of general linear model in case of heteroscedastic errors
Communications in Statistics - Simulation and Computation ( IF 0.9 ) Pub Date : 2020-12-24 , DOI: 10.1080/03610918.2020.1856874
Sajjad Haider Bhatti 1 , Faizan Wajid Khan 2 , Muhammad Irfan 1 , Muhammad Ali Raza 1
Affiliation  

Abstract

Aiming at minimizing the ratio of error with respect to the response variable, the least squares ratio is a relatively new method for estimating the regression parameters. In the current article, the performance of this new approach is compared with the traditional OLS approach in the case when homoscedasticity of errors assumption is violated. A comparison is made through a simulation study using mean square error, mean absolute percentage error, and false acceptance rate as performance measures. It is observed that the least square ratio method outperforms the OLS method in case of moderate or severe heteroscedasticity for all sample sizes and in case of weak or mild heteroscedasticity for relatively small samples. Generally, it is noted that the efficiency of the least squares ratio method increases with an increase in the severity of heteroscedasticity as well as an increase in values of common error variance. The use of the least squares ratio method is recommended in case of mild or moderate to severe heteroscedasticity. Similar results were obtained from two real-life examples.



中文翻译:

一种在异方差误差情况下有效估计一般线性模型的有效方法

摘要

最小二乘比是一种相对较新的回归参数估计方法,旨在最小化相对于响应变量的误差比。在当前文章中,在违反同方差假设的情况下,将这种新方法的性能与传统的 OLS 方法进行了比较。通过使用均方误差、平均绝对百分比误差和错误接受率作为性能度量的模拟研究进行了比较。据观察,在所有样本大小存在中度或严重异方差的情况下,以及在相对较小的样本存在弱或轻度异方差的情况下,最小二乘比法优于 OLS 方法。一般来说,值得注意的是,最小二乘比法的效率随着异方差严重程度的增加以及公共误差方差值的增加而增加。在轻度或中度至重度异方差的情况下,建议使用最小二乘比法。从两个现实生活中的例子中得到了类似的结果。

更新日期:2020-12-24
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