On the Choice of Smoothing Parameter, Threshold and Truncation in Nonparametric Regression by Non-Linear Wavelet Methods
本文为回归均值的非线性小波估计器建立了渐近理论，适用于一般误差分布和设计，重点通过矩条件描述误差分布尾部权重对阈值和截断参数选择的影响，并提出了随机设计校正方法。
SUMMARY Concise asymptotic theory is developed for non-linear wavelet estimators of regression means, in the context of general error distributions, general designs, general normalizations in the case of stochastic design, and non-structural assumptions about the mean. The influence of the tail weight of the error distribution is addressed in the setting of choosing threshold and truncation parameters. Mainly, the tail weight is described in an extremely simple way, by a moment condition; previous work on this topic has generally imposed the much more stringent assumption that the error distribution be normal. Different approaches to correction for stochastic design are suggested. These include conventional kernel estimation of the design density, in which case the interaction between the smoothing parameters of the non-linear wavelet estimator and the linear kernel method is described.