Empirical likelihood for generalized smoothly trimmed mean

Elina Kresse, Emils Silins, Janis Valeinis
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Abstract

This paper introduces a new version of the smoothly trimmed mean with a more general version of weights, which can be used as an alternative to the classical trimmed mean. We derive its asymptotic variance and to further investigate its properties we establish the empirical likelihood for the new estimator. As expected from previous theoretical investigations we show in our simulations a clear advantage of the proposed estimator over the classical trimmed mean estimator. Moreover, the empirical likelihood method gives an additional advantage for data generated from contaminated models. For the classical trimmed mean it is generally recommended in practice to use symmetrical 10\% or 20\% trimming. However, if the trimming is done close to data gaps, it can even lead to spurious results, as known from the literature and verified by our simulations. Instead, for practical data examples, we choose the smoothing parameters by an optimality criterion that minimises the variance of the proposed estimators.
广义平滑修剪均值的经验似然法
本文介绍了一种新版本的平滑修剪均值,其权重版本更为宽泛,可作为经典修剪均值的替代方法。我们推导出了它的渐近方差,为了进一步研究它的特性,我们建立了最新估计器的经验似然。正如之前的理论研究所预期的那样,我们在模拟中显示了所提出的估计器相对于经典修剪均值估计器的明显优势。此外,经验似然法还为污染模型生成的数据提供了额外的优势。对于经典修剪均值,在实践中一般建议使用不对称的 10%或 20%修剪。然而,如果在接近数据间隙的地方进行修剪,甚至会导致虚假结果,这在文献中已有记载,我们的模拟也验证了这一点。相反,对于实际数据示例,我们通过最优化准则来选择平滑参数,使所提出的估计值的方差最小化。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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