Choosing shape parameters for regression in reproducing kernel Hilbert space and variable selection

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Nonparametric Statistics Pub Date : 2023-01-10 DOI:10.1080/10485252.2023.2164890

Xin Tan, Yingcun Xia, Efang Kong

引用次数: 0

Abstract

The Gaussian radial basis function (RBF) is a widely used kernel function in kernel-based methods. The parameter in RBF, referred to as the shape parameter, plays an essential role in model fitting. In this paper, we propose a method to select the shape parameters for the general Gaussian RBF kernel. It can simultaneously serve for variable selection and regression function estimation. For the former, asymptotic consistency is established; for the latter, the estimation is as efficient as if the true or optimal shape parameters are known. Simulations and real examples are used to illustrate the method's performance of prediction by comparing it with other popular methods.

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复现核希尔伯特空间中回归形状参数的选择及变量的选择

高斯径向基函数(Gaussian radial basis function, RBF)是基于核的方法中广泛使用的一种核函数。RBF中的参数称为形状参数，在模型拟合中起着至关重要的作用。本文提出了一种选择一般高斯RBF核形状参数的方法。它可以同时用于变量选择和回归函数估计。对于前者，建立了渐近一致性;对于后者，估计是有效的，如果真实或最优形状参数是已知的。通过仿真和实例，将该方法与其他常用方法进行了比较，说明了该方法的预测性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Nonparametric Statistics 数学-统计学与概率论

CiteScore

1.50

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Nonparametric Statistics provides a medium for the publication of research and survey work in nonparametric statistics and related areas. The scope includes, but is not limited to the following topics: Nonparametric modeling, Nonparametric function estimation, Rank and other robust and distribution-free procedures, Resampling methods, Lack-of-fit testing, Multivariate analysis, Inference with high-dimensional data, Dimension reduction and variable selection, Methods for errors in variables, missing, censored, and other incomplete data structures, Inference of stochastic processes, Sample surveys, Time series analysis, Longitudinal and functional data analysis, Nonparametric Bayes methods and decision procedures, Semiparametric models and procedures, Statistical methods for imaging and tomography, Statistical inverse problems, Financial statistics and econometrics, Bioinformatics and comparative genomics, Statistical algorithms and machine learning. Both the theory and applications of nonparametric statistics are covered in the journal. Research applying nonparametric methods to medicine, engineering, technology, science and humanities is welcomed, provided the novelty and quality level are of the highest order. Authors are encouraged to submit supplementary technical arguments, computer code, data analysed in the paper or any additional information for online publication along with the published paper.