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A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density

机译：具有可变误差密度的非参数回归模型中带宽估计的采样算法

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Nadaraya-Watson (NW) estimator is a popular estimator of regression function in a nonparametric regression model. The performance of the regression function is determined by the choice of bandwidths. The mostly used methods for bandwidth selection for the NW estimator are the rule-of-thumb, cross-validation (CV), plug-in and bootstrapping methods. It may be necessary to examine the distribution of response in the vicinity of the estimated mean. One approach for this is the estimation of kernel density of residuals that are determined by the choice of the bandwidth. This depends on the residuals fitted using NW estimator of the regression function but provides no information about choosing bandwidths in the NW regression estimator, where as the bandwidth selection depends on error distribution. Hence there is no data-driven approach for bandwidth selection for both the estimators together. A sampling algorithm to estimate the bandwidths simultaneously is presented. The bandwidths are treated as parameters and the investigation is done using the parametric approach even though the model is nonparametric. (42 refs.)
机译：Nadaraya-Watson（NW）估计器是非参数回归模型中回归函数的流行估计器。回归函数的性能取决于带宽的选择。 NW估计器最常用的带宽选择方法是经验法则，交叉验证（CV），插件和自举方法。可能有必要检查估计平均值附近的响应分布。一种方法是通过带宽的选择来确定残留的内核密度。这取决于使用回归函数的NW估计器拟合的残差，但不提供有关在NW回归估计器中选择带宽的信息，因为带宽选择取决于误差分布。因此，对于两个估计器一起，没有数据驱动的带宽选择方法。提出了一种同时估计带宽的采样算法。带宽被视为参数，并且即使模型是非参数的，也使用参数方法进行调查。 （42篇参考文献）

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