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Density estimation in the presence of noise

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  • Walter, Gilbert G.

Abstract

The problem of density estimation in the absence of noise has been widely studied and is well known. However if noise is added to the sample, the procedure must be modified by incorporating a deconvolution. In this paper we do so by using a procedure similar to empirical Bayes estimation which involves band-limited wavelets. Rates of mean square convergence are found under various hypotheses.

Suggested Citation

  • Walter, Gilbert G., 1999. "Density estimation in the presence of noise," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 237-246, February.
    • Handle: RePEc:eee:stapro:v:41:y:1999:i:3:p:237-246
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    Cited by:

    1. Pensky, Marianna, 2002. "Density deconvolution based on wavelets with bounded supports," Statistics & Probability Letters, Elsevier, vol. 56(3), pages 261-269, February.
    2. Martin L. Hazelton & Berwin A. Turlach, 2010. "Semiparametric Density Deconvolution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 91-108, March.
    3. Harry Zanten & Pawel Zareba, 2008. "A note on wavelet density deconvolution for weakly dependent data," Statistical Inference for Stochastic Processes, Springer, vol. 11(2), pages 207-219, June.
    4. Liu, Youming & Wu, Cong, 2019. "Point-wise estimation for anisotropic densities," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 112-125.

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