论文标题
通过拉瓜系列的非参数回归模型的估计模型，具有添加剂和乘法噪声
Estimation in nonparametric regression model with additive and multiplicative noise via Laguerre series
论文作者
论文摘要
我们研究了具有添加剂和乘法噪声的非参数回归估计，并基于Laguerre系列构造自适应阈值估计器。当未知函数属于Laguerre-Sobolev空间时，所提出的方法在渐近地达到了近乎最佳的收敛速率。我们考虑两个噪声结构下的问题。 （1）{i.i.d.}高斯错误和（2）长期内存高斯错误。在{i.i.d.}情况下，我们的收敛速率与文献中的收敛率相似。在长期内存的情况下，仅当长期内存在任何一个噪声源中足够强时，收敛速率都取决于长期内存参数，否则，速率与{i.i.d.}噪声下的速度相同。
We look into the nonparametric regression estimation with additive and multiplicative noise and construct adaptive thresholding estimators based on Laguerre series. The proposed approach achieves asymptotically near-optimal convergence rates when the unknown function belongs to Laguerre-Sobolev space. We consider the problem under two noise structures; (1) { i.i.d.} Gaussian errors and (2) long-memory Gaussian errors. In the { i.i.d.} case, our convergence rates are similar to those found in the literature. In the long-memory case, the convergence rates depend on the long-memory parameters only when long-memory is strong enough in either noise source, otherwise, the rates are identical to those under { i.i.d.} noise.
