基于局部多项式展开的多元非参数模型贝叶斯带宽选择

在多元非参数模型中带宽和阶的选择对局部多项式估计量的表现十分重要。本文基于交叉验证准则提出一个自适应贝叶斯带宽选择方法。在给定的误差密度函数下,该方法可推导出对应的似然函数,并构造带宽参数的后验密度函数。随后,通过带宽的后验期望可同时获得阶和带宽的估计。数值模拟的结果表明,该方法不仅比大拇指准则方法精确,且比交叉验证方法耗时更少。与此同时,与Nadaraya-Watson估计相比,所提带宽选择方法对多元非参数模型的适应性要更好。最后,本文通过一组实际数据说明有限样本下所提贝叶斯带宽选择的表现很好。

Bayesian Bandwidth Selection for Multivariate Nonparametric Regression Models Based on Local Polynomial Expansion

The selection of bandwidth parameters and the order is a very important step in determining the performance of local polynomial estimator in multivariate nonparametric models.An adaptive Bayesian bandwidth selection approach based on cross-validation criterion is proposed in this paper.Under the given error density function,the proposed method can be used to derive the corresponding likelihood function and construct the posterior of bandwidth parameters.Then,the estimation of the bandwidth and the order can be obtained by the posterior expectation of the bandwidth.The results of numerical simulations show that the proposed approach achieves more accuracy than the rule-of-thumb,and takes shorter time than cross-validation.Furthermore,compared to Nadaraya-Watson estimator,the proposed bandwidth selection approach adapts better to multivariate nonparametric models.Finally,a real example is presented to illustrate the finite sample performance of the proposed Bayesian bandwidth selection method is well.