A Bayesian method to estimate the optimal bandwidth for multivariate kernel estimator
A Bayesian method to estimate the optimal bandwidth for multivariate kernel estimator
复制标题
一种估计多元核估计器最优带宽的贝叶斯方法
DOI：
10.1080/10485252.2010.485200
复制
发表时间：
2011
影响因子：
1.2
通讯作者：
G. S. Atuncar
中科院分区：
文献类型：
--
作者：
Max Sousa de Lima;G. S. Atuncar
用核方法估计多变量密度具有广泛的适用性。然而，与单变量情况相比，这一问题受到的关注较少。这主要是由于估计最优平滑矩阵的难度越来越大，特别是当组件相关时。为了克服这一困难，本文提出了一种估计最优平滑矩阵H的贝叶斯方法。定义了损失函数，H的估计量是使损失函数最小的矩阵。我们进行了具有相关性的多元密度混合模拟，结果非常令人满意。
The estimation of multivariate densities using the kernel method has wide applicability. However, this problem has received less attention than the univariate case. This is mainly due to the increasing difficulty in estimating the optimal smoothing matrix, especially when the components are correlated. To overcome this difficulty, we propose in this work a Bayesian method to estimate the optimal smoothing matrix H. A loss function is defined and the estimator of H is the matrix minimising the loss function. We carried out simulations with a mixture of multivariate densities with correlation and the results were highly satisfactory.