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A new Bayesian wavelet thresholding estimator of nonparametric regression

Author

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  • M. Afshari
  • F. Lak
  • B. Gholizadeh

Abstract

The methods of estimation of nonparametric regression function are quite common in statistical application. In this paper, the new Bayesian wavelet thresholding estimation is considered. The new mixture prior distributions for the estimation of nonparametric regression function by applying wavelet transformation are investigated. The reversible jump algorithm to obtain the appropriate prior distributions and value of thresholding is used. The performance of the proposed estimator is assessed with simulated data from well-known test functions by comparing the convergence rate of the proposed estimator with respect to another by evaluating the average mean square error and standard deviations. Finally by applying the developed method, density function of galaxy data is estimated.

Suggested Citation

  • M. Afshari & F. Lak & B. Gholizadeh, 2017. "A new Bayesian wavelet thresholding estimator of nonparametric regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(4), pages 649-666, March.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:4:p:649-666
    DOI: 10.1080/02664763.2016.1182130
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    1. repec:dau:papers:123456789/1908 is not listed on IDEAS
    2. F. Abramovich & T. Sapatinas & B. W. Silverman, 1998. "Wavelet thresholding via a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 725-749.
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    Cited by:

    1. Karamikabir, Hamid & Afshari, Mahmoud, 2020. "Generalized Bayesian shrinkage and wavelet estimation of location parameter for spherical distribution under balance-type loss: Minimaxity and admissibility," Journal of Multivariate Analysis, Elsevier, vol. 177(C).

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