Expectiles have gained considerable attention in recent years due to wide applications in many areas. In this study, the k-nearest neighbours approach, together with the asymmetric least squares loss function, called ex-$kNN$, is proposed for computing expectiles. Firstly, the effect of various distance measures on ex-$kNN$ in terms of test error and computational time is evaluated. It is found that Canberra, Lorentzian, and Soergel distance measures lead to minimum test error, whereas Euclidean, Canberra, and Average of $(L_1,L_{\infty })$ lead to a low computational cost. Secondly, the performance of ex-$kNN$ is compared with existing packages er-boost and ex-svm for computing expectiles that are based on nine real life examples. Depending on the nature of data, the ex-$kNN$ showed two to 10 times better performance than er-boost and comparable performance with ex-svm regarding test error. Computationally, the ex-$kNN$ is found two to five times faster than ex-svm and much faster than er-boost, particularly, in the case of high dimensional data.

中文翻译：

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使用k最近邻方法计算期望值

由于在许多领域中的广泛应用，近年来，小球获得了相当大的关注。在这项研究中，k最近邻方法与不对称最小二乘损失函数（称为ex-$ķññ$被提议用于计算期望值。首先，各种距离测量对防爆的影响$ķññ$根据测试误差和计算时间进行评估。发现堪培拉，洛伦兹和Soergel距离测度导致最小的测试误差，而欧几里得，堪培拉和Average的平均值$（{\mathrm{大号}}_{\mathrm{1个}}，{\mathrm{大号}}_{\infty }）$导致较低的计算成本。其次，前$ķññ$将其与现有软件包er-boost和ex-svm进行比较，这些软件包基于9个现实生活中的例子计算出期望值。根据数据的性质，$ķññ$显示出的性能比er-boost高出2到10倍，并且在测试错误方面与ex-svm相当。根据计算，$ķññ$ 发现它比ex-svm快2至5倍，比er-boost快得多，特别是在高维数据的情况下。