论文标题
通过傅立叶积分定理和傅立叶内核进行多元平滑
Multivariate Smoothing via the Fourier Integral Theorem and Fourier Kernel
论文作者
论文摘要
从傅立叶积分定理开始，我们提出了多元函数的自然蒙特卡洛估计量，包括密度，混合密度，过渡密度，回归函数以及寻找多变量密度函数模式（模态回归）。建立了收敛速度，在许多情况下，在基于内核的当前标准估计器（包括内核密度估计器和内核回归函数）中提供了较高的速率。提出了数值插图。
Starting with the Fourier integral theorem, we present natural Monte Carlo estimators of multivariate functions including densities, mixing densities, transition densities, regression functions, and the search for modes of multivariate density functions (modal regression). Rates of convergence are established and, in many cases, provide superior rates to current standard estimators such as those based on kernels, including kernel density estimators and kernel regression functions. Numerical illustrations are presented.
