Confidence sets for nonparametric wavelet regression
Confidence sets for nonparametric wavelet regression
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DOI：
10.1214/009053605000000011
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发表时间：
2005-04-01
影响因子：
4.5
通讯作者：
Wasserman, L
中科院分区：
文献类型：
--
作者：
Genovese, CR;Wasserman, L
我们使用在Besov球上一致的小波构造回归函数的非参数置信集。我们同时考虑了小波系数的阈值和调制估计器。通过证明由损失函数构造的枢轴过程一致收敛于均值零高斯过程，得到了置信度集。对这个枢轴进行倒置得到小波系数的置信度，由此我们得到回归曲线泛函的置信度集。
We construct nonparametric confidence sets for regression functions using wavelets that are uniform over Besov balls. We consider both thresholding and modulation estimators for the wavelet coefficients. The confidence set is obtained by showing that a pivot process, constructed from the loss function, converges uniformly to a mean zero Gaussian process. Inverting this pivot yields a confidence set for the wavelet coefficients, and from this we obtain confidence sets on functionals of the regression curve.