On Variance-Stabilizing Multivariate Non Parametric Regression Estimation
On Variance-Stabilizing Multivariate Non Parametric Regression Estimation
复制标题
方差稳定多元非参数回归估计
DOI：
10.1080/03610926.2013.775298
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Yuichiro Kanazawa
中科院分区：
文献类型：
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作者：
Kiheiji Nishida;Yuichiro Kanazawa
单变量局部线性估计量（LL）的均方误差（MSE）最小化局部变量带宽是众所周知的。该带宽不稳定域上的方差。此外，在回归函数具有零曲率的区域中，LL估计是不连续的。在本文中，我们提出了一个方差稳定（VS）的局部可变对角带宽矩阵的多元LL估计。理论上，VS带宽可以优于MSE最小化局部变量标量带宽的多变量扩展的渐近平均积分平方误差，并可以避免由MSE最小化带宽创建的不连续性。我们提出了一种算法估计VS带宽和仿真研究。
The mean squared error (MSE)-minimizing local variable bandwidth for the univariate local linear estimator (the LL) is well-known. This bandwidth does not stabilize variance over the domain. Moreover, in regions where a regression function has zero curvature, the LL estimator is discontinuous. In this paper, we propose a variance-stabilizing (VS) local variable diagonal bandwidth matrix for the multivariate LL estimator. Theoretically, the VS bandwidth can outperform the multivariate extension of the MSE-minimizing local variable scalar bandwidth in terms of asymptotic mean integrated squared error and can avoid discontinuity created by the MSE-minimizing bandwidth. We present an algorithm for estimating the VS bandwidth and simulation studies.