论文标题
模态线性回归的内核选择：最佳内核和IRLS算法
Kernel Selection for Modal Linear Regression: Optimal Kernel and IRLS Algorithm
论文作者
论文摘要
模态线性回归（MLR）是一种获得条件模式预测器作为线性模型的方法。我们从两个角度研究了MLR的内核选择：“哪些内核达到较小的错误？”和“哪个内核在计算上有效？”。首先，我们表明，在最小化所得MLR参数的渐近平方平方误差的意义上，双重内核是最佳的。该结果来自我们对MLR渐近统计行为的精致分析。其次，我们提供一个内核类别，迭代重新加权最小二乘算法（IRLS）保证会收敛，尤其是证明具有Epanechnikov内核的IRL在有限数量的迭代次数中终止。仿真研究从经验上证明，使用双重核提供了良好的估计准确性，并且使用Epanechnikov内核具有计算效率。我们的结果改善了MLR，其中现有研究通常坚持使用核心选择的指南，而专门针对它的高斯内核和模态EM算法。
Modal linear regression (MLR) is a method for obtaining a conditional mode predictor as a linear model. We study kernel selection for MLR from two perspectives: "which kernel achieves smaller error?" and "which kernel is computationally efficient?". First, we show that a Biweight kernel is optimal in the sense of minimizing an asymptotic mean squared error of a resulting MLR parameter. This result is derived from our refined analysis of an asymptotic statistical behavior of MLR. Secondly, we provide a kernel class for which iteratively reweighted least-squares algorithm (IRLS) is guaranteed to converge, and especially prove that IRLS with an Epanechnikov kernel terminates in a finite number of iterations. Simulation studies empirically verified that using a Biweight kernel provides good estimation accuracy and that using an Epanechnikov kernel is computationally efficient. Our results improve MLR of which existing studies often stick to a Gaussian kernel and modal EM algorithm specialized for it, by providing guidelines of kernel selection.
