论文标题
在带宽两个带宽的Nadaraya-Watson估计器上
On a Nadaraya-Watson Estimator with Two Bandwidths
论文作者
论文摘要
在回归模型中，我们将回归函数的Nadaraya-Watson估计值写为两个内核估计器的商，并为分子和分母提出了一种带宽选择方法。我们证明了数据驱动的估计器和结果比率的风险界限。模拟研究证实，与通过带宽的交叉验证选择相比，这两个估计器的性能都良好。然而，出乎意料的是，在小噪声环境中，发现单带宽跨验估估计器要比前两个良好估计器的比率好得多。但是，这两种方法在噪声较大的模型中具有相似的性能。
In a regression model, we write the Nadaraya-Watson estimator of the regression function as the quotient of two kernel estimators, and propose a bandwidth selection method for both the numerator and the denominator. We prove risk bounds for both data driven estimators and for the resulting ratio. The simulation study confirms that both estimators have good performances, compared to the ones obtained by cross-validation selection of the bandwidth. However, unexpectedly, the single-bandwidth cross-validation estimator is found to be much better than the ratio of the previous two good estimators, in the small noise context. However, the two methods have similar performances in models with large noise.
