In this paper, we propose a novel asymmetric $ϵ$-insensitive pinball loss function for quantile estimation. There exists some pinball loss functions which attempt to incorporate the $ϵ$-insensitive zone approach in it but, they fail to extend the $ϵ$-insensitive approach for quantile estimation in true sense. The proposed asymmetric $ϵ$-insensitive pinball loss function can make an asymmetric $ϵ$- insensitive zone of fixed width around the data and divide it using $\tau$ value for the estimation of the $\tau$th quantile. The use of the proposed asymmetric $ϵ$-insensitive pinball loss function in Support Vector Quantile Regression (SVQR) model improves its prediction ability significantly. It also brings the sparsity back in SVQR model. Further, the numerical results obtained by several experiments carried on simulated and real world datasets empirically show the efficacy of the proposed ‘$ϵ$-Support Vector Quantile Regression’ ($ϵ$-SVQR) model over other existing SVQR models.

在本文中，我们提出了一种新颖的非对称 $ϵ$-不敏感的弹球丢失功能，用于分位数估计。存在一些弹球丢失功能，这些功能试图合并$ϵ$-不敏感区域方法，但是它们无法扩展 $ϵ$-不敏感的方法，用于真正意义上的分位数估计。建议的不对称$ϵ$-不灵敏的弹球丢失功能会使不对称 $ϵ$-数据周围固定宽度的不敏感区域，并使用 $\tau$ 估计值 $\tau$分位数。建议使用不对称$ϵ$支持向量分位数回归（SVQR）模型中的非敏感弹球丢失功能大大提高了其预测能力。它还将稀疏性带回到了SVQR模型中。此外，通过在模拟和现实世界数据集上进行的几次实验获得的数值结果凭经验表明了提出的“$ϵ$-支持向量分位数回归（$ϵ$-SVQR）模型。