论文标题
复制基于内核的非参数回归方案
Reproducing kernels based schemes for nonparametric regression
论文作者
论文摘要
在这项工作中，我们开发并研究了解决非参数回归问题的经验投影操作方案。该方案基于在合适的繁殖内核希尔伯特空间（RKHS）上对回归函数的近似投影。本文中考虑的RKHS是由Legendre Christoffel-Darboux和卷积SINC内核提供的Mercer内核产生的。在假设回归函数属于某些合适的功能空间的假设下，我们提供了误差和收敛分析。我们还考虑了流行的RKHS正式最小化的最小化，以进行非参数回归。特别是，我们检查了第二个方案的数值稳定性，并在SINC内核的特殊情况下提供了其收敛速率。最后，我们通过各种数值模拟说明了提出的方法。
In this work, we develop and study an empirical projection operator scheme for solving nonparametric regression problems. This scheme is based on an approximate projection of the regression function over a suitable reproducing kernel Hilbert space (RKHS). The RKHS considered in this paper are generated by the Mercer kernels given by the Legendre Christoffel-Darboux and convolution Sinc kernels. We provide error and convergence analysis of the proposed scheme under the assumption that the regression function belongs to some suitable functional spaces. We also consider the popular RKHS regularized least square minimization for nonparametric regression. In particular, we check the numerical stability of this second scheme and we provide its convergence rate in the special case of the Sinc kernel. Finally, we illustrate the proposed methods by various numerical simulation.
