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Wavelet Estimation of an Unknown Function Observed with Correlated Noise

Wang, Xue, Wood, Andrew T.A. (2010) Wavelet Estimation of an Unknown Function Observed with Correlated Noise. Communications in Statistics - Simulation and Computation, 39 (2). pp. 287-304. ISSN 0361-0918. (doi:10.1080/03610910903443972)

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In many practical applications of nonparametric regression, it is desirable to allow for the possibility that the noise is correlated. In this paper, we focus on wavelet-based nonparametric function estimation and propose two distinct methods for estimating the correlation structure of the noise, one based in the time domain and the other based in the wavelet domain. Once the correlation structure has been estimated, there are various methods that may be used for reconstructing the unknown signal; we focus here on the empirical Bayes block shrinkage method proposed by Wang and Wood (2006). A simulation study is described. Our numerical results indicate that the proposed methods do a good job of reconstructing the signal even when the noise is highly correlated.

Item Type: Article
DOI/Identification number: 10.1080/03610910903443972
Uncontrolled keywords: Bayes block shrinkage; Correlation structure; Durbin-Levinson algorithm; innovations algorithm; pseudo likelihood estimation.
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Xue Wang
Date Deposited: 05 Dec 2013 11:50 UTC
Last Modified: 29 May 2019 11:34 UTC
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