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首页> 外文期刊>Journal of Uncertainty Analysis and Applications >Estimation of a linear model with two-parameter symmetric platykurtic distributed errors
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Estimation of a linear model with two-parameter symmetric platykurtic distributed errors

机译：具有双参数对称平板分布式错误的线性模型的估计

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Purpose A linear regression model with Gaussian-distributed error terms is the most widely used method to describe the possible relationship between outcome and predictor variables. However, there are some drawbacks of Gaussian errors such as the distribution being mesokurtic. In many practical situations, the variables under study may not be mesokurtic but are platykurtic. Hence, to analyze this sort of platykurtic variables, a multiple regression model with symmetric platykurtic (SP) distributed errors is needed. In this paper, we introduce and develop a multiple linear regression model with symmetric platykurtic distributed errors for the first time. Methods We used the methods of ordinary least squares (OLS) and maximum likelihood (ML) to estimate the model parameters. The properties of the ML estimators with respect to the symmetric platykurtic distributed errors are discussed. The model selection criteria such as Akaike information criteria (AIC) and Bayesian information criteria (BIC) for the models are used. The utility of the proposed model is demonstrated with both simulation and real-time data. Results A comparative study of symmetric platykurtic linear regression model with the Gaussian model revealed that the former gives good fit to some data sets. The results also revealed that ML estimators are more efficient than OLS estimators in terms of the relative efficiency of the one-step-ahead forecast mean square error. Conclusions The study shows that the symmetric platykurtic distribution serves as an alternative to the normal distribution. The developed model is useful for analyzing data sets arising from agricultural experiments, portfolio management, space experiments, and a wide range of other practical problems.
机译：目的，具有高斯分布式错误术语的线性回归模型是描述结果和预测变量之间可能的关系的最广泛使用的方法。然而，诸如中间型诸如分布的高斯误差存在一些缺点。在许多实际情况下，研究中的变量可能不是间隙，而是属platykurtic。因此，为了分析这种平板曲率变量，需要具有对称性PlatyKurtic（SP）分布式错误的多元回归模型。在本文中，我们首次介绍并开发了一个具有对称性PlatyKurtic分布式错误的多元线性回归模型。方法使用普通最小二乘（OLS）的方法和最大似然（ML）来估计模型参数。讨论了M1估计相对于对称的平板分布式误差的性质。使用模型选择标准，例如模型的Akaike信息标准（AIC）和贝叶斯信息标准（BIC）。仿真和实时数据展示了所提出的模型的效用。结果与高斯模型对称平板线性回归模型的比较研究表明，前者给予一些数据集。结果还显示ML估计变得比OLS估计值更有效，就一步预测均方误差的相对效率而言。结论该研究表明，对称的平板抗性分配作为正态分布的替代品。开发的模型可用于分析来自农业实验，投资组合管理，空间实验以及各种其他实际问题的数据集。

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