Nonparametric deconvolution problem for dependent sequences
Nonparametric deconvolution problem for dependent sequences
复制标题
DOI：
10.1214/07-ejs154
复制
发表时间：
2007-11
影响因子：
1.1
通讯作者：
Rafal Kulik
中科院分区：
文献类型：
--
作者：
Rafal Kulik
本文考虑了具有噪声观测的弱相依和强相依过程密度函数的非参数估计。我们表明，在普通的光滑的情况下，最佳带宽的选择可以影响到长范围的依赖性，相反的标准情况下，当没有噪声存在。特别是，如果依赖是moder- ate带宽，均方收敛率，此外，中心极限定理是相同的，在i.i.d.案子如果相关性足够强，则带宽选择受相关性强度的影响，这与无噪声情况相比是不同的。还有，
We consider the nonparametric estimation of the density func- tion of weakly and strongly dependent processes with noisy observations. We show that in the ordinary smooth case the optimal bandwidth choice can be influenced by long range dependence, as opposite to the standard case, when no noise is present. In particular, if the dependence is moder- ate the bandwidth, the rates of mean-square convergence and, additionally, central limit theorem are the same as in the i.i.d. case. If the dependence is strong enough, then the bandwidth choice is influenced by the strength of dependence, which is dierent when compared to the non-noisy case. Also,