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Wavelet regression with correlated errors on a piecewise Hölder class

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  • Porto, Rogério F.
  • Morettin, Pedro A.
  • Aubin, Elisete C.Q.

Abstract

This paper generalizes the methodology of Cai and Brown [Cai, T., Brown, L.D., 1998. Wavelet shrinkage for nonequispaced samples. The Annals of Statistics 26, 1783-1799] for wavelet shrinkage for nonequispaced samples, but in the presence of correlated stationary Gaussian errors. If the true function is a member of a piecewise Hölder class, it is shown that, even for long memory errors, the rate of convergence of the procedure is almost-minimax relative to the independent and identically distributed errors case.

Suggested Citation

  • Porto, Rogério F. & Morettin, Pedro A. & Aubin, Elisete C.Q., 2008. "Wavelet regression with correlated errors on a piecewise Hölder class," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2739-2743, November.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:16:p:2739-2743
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    References listed on IDEAS

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    1. Iain M. Johnstone & Bernard W. Silverman, 1997. "Wavelet Threshold Estimators for Data with Correlated Noise," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 319-351.
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    1. Marcelo M. Taddeo & Pedro A. Morettin, 2023. "Bayesian P-Splines Applied to Semiparametric Models with Errors Following a Scale Mixture of Normals," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1331-1355, August.
    2. Salcedo, Gladys E. & Porto, Rogério F. & Morettin, Pedro A., 2012. "Comparing non-stationary and irregularly spaced time series," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3921-3934.
    3. Duván Humberto Cataño & Carlos Vladimir Rodríguez-Caballero & Daniel Peña, 2019. "Wavelet Estimation for Dynamic Factor Models with Time-Varying Loadings," CREATES Research Papers 2019-23, Department of Economics and Business Economics, Aarhus University.

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