Research PapersNo Access

A note on wavelet deconvolution density estimation

Xiaochen Zeng

Department of Applied Mathematics, Beijing University of Technology, Pingle Yuan 100, Beijing 100124, P. R. China

E-mail Address: zengxiaochen@emails.bjut.edu.cn

https://doi.org/10.1142/S0219691317500552Cited by:8 (Source: Crossref)

Abstract

This paper discusses the uniformly strong convergence of multivariate density estimation with moderately ill-posed noise over a bounded set. We provide a convergence rate over Besov spaces by using a compactly supported wavelet. When the model degenerates to one-dimensional noise-free case, the convergence rate coincides with that of Giné and Nickl’s (Ann. Probab., 2009 or Bernoulli, 2010). Our result can also be considered as an extension of Masry’s theorem (Stoch. Process. Appl., 1997) to some extent.

Keywords:

AMSC: 42C40, 62G07, 62G20

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