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摘要翻译：
我们考虑了具有噪声观测的弱依赖和强依赖过程密度函数的非参数估计。我们证明了在普通平滑情况下，与标准情况相反，当无噪声时，最优带宽的选择会受到长程依赖性的影响。特别地，如果对带宽的依赖程度适中，则均方收敛速度和中心极限定理与I.I.D.中的均方收敛速度和中心极限定理是相同的。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。中心极限定理还受到依赖强度的影响。另一方面，如果密度是超mooth，那么长程依赖对最优带宽的选择没有任何影响。
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英文标题：
《Nonparametric deconvolution problem for dependent sequences》
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作者：
Rafa{\l} Kulik
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
We consider the nonparametric estimation of the density function 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 moderate 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 different when compared to the non-noisy case. Also, central limit theorem are influenced by the strength of dependence. On the other hand, if the density is supersmooth, then long range dependence has no effect at all on the optimal bandwidth choice.
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PDF链接：
https://arxiv.org/pdf/711.4004
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