Multichannel deconvolution with long range dependence: upper bounds on the Lp-risk (1 ≤ p < ∞)

Rafal Kulik, Theofanis Sapatinas, Justin Rory Wishart*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We consider multichannel deconvolution in a periodic setting with long-memory errors under three different scenarios for the convolution operators, i.e., super-smooth, regular-smooth and box-car convolutions. We investigate global performances of linear and hard-thresholded non-linear wavelet estimators for functions over a wide range of Besov spaces and for a variety of loss functions defining the risk. In particular, we obtain upper bounds on convergence rates using the Lp-risk (1≤ < ∞). Contrary to the case where the errors follow independent Brownian motions, it is demonstrated that multichannel deconvolution with errors that follow independent fractional Brownian motions with different Hurst parameters results in a much more involved situation. An extensive finite-sample numerical study is performed to supplement the theoretical findings.

Original languageEnglish
Pages (from-to)357-384
Number of pages28
JournalApplied and Computational Harmonic Analysis
Issue number3
Publication statusPublished - May 2015
Externally publishedYes


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