Kernel-based modal statistical methods include mode estimation, regression, and clustering. Estimation accuracy of these methods depends on the kernel used as well as the bandwidth. We study effect of the selection of the kernel function to the estimation accuracy of these methods. In particular, we theoretically show a (multivariate) optimal kernel that minimizes its analytically-obtained asymptotic error criterion when using an optimal bandwidth, among a certain kernel class defined via the number of its sign changes.

翻译：基于核函数的模态统计方法包括众数估计、回归与聚类。这些方法的估计精度取决于所选核函数及带宽。本文研究核函数选择对上述方法估计精度的影响。具体而言，我们在通过符号变化次数定义的特定核函数类中，从理论上证明了当使用最优带宽时，能够使解析获得的渐近误差准则最小化的（多变量）最优核函数。