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Adaptive Wavelet Density Estimation under Independence Hypothesis
  • Kaikai Cao,
  • Xiaochen Zeng
Kaikai Cao
Weifang University
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Xiaochen Zeng
Beijing University of Technology
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Abstract

Based on a data-driven selection of an estimator from a fixed family of kernel estimators, Goldenshluger \& Lepski (2014) considered the problem of adaptive minimax un-compactly supported density estimation on $\mathbb{R}^{d}$ with $L^{p}$ risk over Nikol’skii classes. This paper shows the same convergence rates by using a data-driven wavelet estimator over Besov spaces, because the wavelet estimations provide more local information and fast algorithm. Moreover, we provide better convergence rates under the independence hypothesis, which reduces the dimension disaster effectively.

Peer review status:UNDER REVIEW

30 Sep 2020Submitted to Mathematical Methods in the Applied Sciences
01 Oct 2020Submission Checks Completed
01 Oct 2020Assigned to Editor
17 Oct 2020Reviewer(s) Assigned
24 Jan 2021Review(s) Completed, Editorial Evaluation Pending
24 Jan 2021Editorial Decision: Revise Major
07 Feb 20211st Revision Received
07 Feb 2021Submission Checks Completed
07 Feb 2021Assigned to Editor
27 Feb 2021Reviewer(s) Assigned