Local polynomial variance-function estimation
Local polynomial variance-function estimation
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DOI：
10.2307/1271131
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发表时间：
1997-08
期刊：
影响因子：
2.5
通讯作者：
D. Ruppert;M. Wand;U. Holst;O. Hössjer
中科院分区：
文献类型：
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作者：
D. Ruppert;M. Wand;U. Holst;O. Hössjer
异方差非参数回归模型中的条件方差函数是通过残差平方的线性平滑来估计的。注意力集中在局部多项式平滑。假设均值和方差函数都是光滑的，但都不假设是在一个参数族中。研究了均值初步估计的偏差效应，提出了一种自由度偏差修正方法。校正的方法被证明是自适应的，在这个意义上，方差函数可以估计相同的渐近均值和方差，如果均值函数是已知的。一个建议是使用标准的带宽选择器估计的均值和方差函数。该建议说明了从激光雷达测量大气污染物的方法和从双折射模型计算的数据。
The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focused on local polynomial smoothers. Both the mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The biasing effect of preliminary estimation of the mean is studied, and a degrees-of-freedom correction of bias is proposed. The corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known. A proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions. The proposal is illustrated with data from the LIDAR method of measuring atmospheric pollutants and from turbulence-model computations.