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Logspline Deconvolution in Besov Space

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  • Ja‐Yong Koo

Abstract

ABSTRACT. In this paper we consider logspline density estimation for random variables which are contaminated with random noise. In the logspline density estimation for data without noise, the logarithm of an unknown density function is estimated by a polynomial spline, the unknown parameters of which are given by maximum likelihood. When noise is present, B‐splines and the Fourier inversion formula are used to construct the logspline density estimator of the unknown density function. Rates of convergence are established when the log‐density function is assumed to be in a Besov space. It is shown that convergence rates depend on the smoothness of the density function and the decay rate of the characteristic function of the noise. Simulated data are used to show the finite‐sample performance of inference based on the logspline density estimation.

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  • Ja‐Yong Koo, 1999. "Logspline Deconvolution in Besov Space," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(1), pages 73-86, March.
    • Handle: RePEc:bla:scjsta:v:26:y:1999:i:1:p:73-86
    DOI: 10.1111/1467-9469.00138
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    Cited by:

    1. Jérémie Bigot & Sébastien Van Bellegem, 2009. "Log‐density Deconvolution by Wavelet Thresholding," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 749-763, December.
    2. Abdous, Belkacem & Germain, Stéphane & Ghazzali, Nadia, 2002. "A unified treatment of direct and indirect estimation of a probability density and its derivatives," Statistics & Probability Letters, Elsevier, vol. 56(3), pages 239-250, February.

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