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首页> 外文会议>WSEAS International Conference on Applied Computer and Applied Computational Science >Robust Estimation of Regression Parameters with Heteroscedastic Errors in the Presence of Outliers
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Robust Estimation of Regression Parameters with Heteroscedastic Errors in the Presence of Outliers

机译：在异常值存在下具有异源误差的回归参数的鲁棒估计

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For generation, statistics practitioners have been relying on the ordinary least squares (OLS) method in the linear regression model due to its optimal properties and ease of computation. The OLS gives unbiased and minimum variance among all unbiased linear estimators when the errors are independent, identically and normally distributed with mean 0 and constant variance σ~2. The homogeneity of error variances (homoscedasticity) is an important assumption in linear regression for which the least squares estimators enjoy the minimum variance property. However, in practice it is difficult to retain the error variance homogeneous for many practical reasons and thus there arises the problem of heteroscedasticity. We generally apply the weighted least squares (WLS) procedure to estimate the regression parameters when heteroscedasticity occurs in the data. The WLS is equivalent to performing the ordinary least squares (OLS) on the transformed variables. However, there is evidence that the WLS estimators are easily affected by a few atypical observations that we often call outliers. In this paper we take the initiative to remedy these two problems simultaneously. We have proposed a robust procedure for the estimation of regression parameters in the presence of heteroscedasticity and outliers. Here we have employed robust techniques twice, once in estimating the group variances and again in determining weights for the least squares. We call this method robust weighted least squares (RWLS). The performance of the newly proposed method is investigated extensively by real data sets and Monte Carlo simulations. The results of the study indicate that the RWLS method is more efficient than the existing methods.
机译：对于代代，由于其最佳性能和易于计算，统计从业者一直依赖于线性回归模型中的普通最小二乘（OLS）方法。当误差独立的情况下，OLS在所有无偏见的线性估计中提供了不偏见的和最小方差，并且通常以平均值0和恒定方差σ〜2分布。误差差异（同性化性能）的均匀性是线性回归中最小二乘估计符享有最小方差性的重要假设。然而，在实践中，难以以许多实际原因均匀地保持误差方差，因此出现了异源性的问题。我们通常将加权最小二乘（WLS）过程应用于当在数据中发生异源性度时估计回归参数。 WLS等同于在变换变量上执行普通的最小二乘（OLS）。然而，有证据表明，WLS估计变得容易受到我们经常呼叫异常值的一些非典型观测的影响。在本文中，我们主动同时解决这两个问题。我们提出了一种稳健的过程，用于在存在异源性和异常值存在下估计回归参数。在这里，我们在估计组差异时两次使用稳健的技术，并且再次在确定最小二乘法的重量时。我们称该方法强大加权最小二乘（RWL）。通过真实数据集和蒙特卡罗模拟广泛地研究了新提出的方法的性能。研究结果表明，RWLS方法比现有方法更有效。

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