On estimation of $$L_{r}$$-norms in Gaussian white noise models
On estimation of $$L_{r}$$-norms in Gaussian white noise models
复制标题
高斯白噪声模型中 $$L_{r}$$-范数的估计
DOI：
10.1007/s00440-020-00982-x
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发表时间：
2020
影响因子：
2
通讯作者：
Mukherjee, Rajarshi
中科院分区：
文献类型：
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作者：
Han, Yanjun;Jiao, Jiantao;Mukherjee, Rajarshi
本文给出了Nikolskiii-Besov空间上高斯白色噪声模型中均值范数的渐近Minimax估计。在这方面，我们补充了Lepski等人的工作（Probab Theory Relat Fields 113（2）：221-253，1999），他们考虑了Hölder空间上的（上界和下界之间有多对数间隙）和dreven（上界和下界渐近尖锐）的情况。我们还考虑了渐进自适应极大极小估计的情况，并证明了研究者在不支付罚款的情况下产生渐进自适应极大极小估计量的能力的偶项和非偶项之间的差异。
We provide a complete picture of asymptotically minimax estimation of-norms (for any) of the mean in Gaussian white noise model over Nikolskii–Besov spaces. In this regard, we complement the work of Lepski et al. (Probab Theory Relat Fields 113(2):221–253, 1999), who considered the cases of(with poly-logarithmic gap between upper and lower bounds) andreven (with asymptotically sharp upper and lower bounds) over Hölder spaces. We additionally consider the case of asymptotically adaptive minimax estimation and demonstrate a difference between even and non-evenrin terms of an investigator’s ability to produce asymptotically adaptive minimax estimators without paying a penalty.