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Density estimation in the uniform deconvolution model

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  • P. Groeneboom
  • G. Jongbloed

Abstract

We consider the problem of estimating a probability density function based on data that are corrupted by noise from a uniform distribution. The (nonparametric) maximum likelihood estimator for the corresponding distribution function is well defined. For the density function this is not the case. We study two nonparametric estimators for this density. The first is a type of kernel density estimate based on the empirical distribution function of the observable data. The second is a kernel density estimate based on the MLE of the distribution function of the unobservable (uncorrupted) data.

Suggested Citation

  • P. Groeneboom & G. Jongbloed, 2003. "Density estimation in the uniform deconvolution model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(1), pages 136-157, February.
    • Handle: RePEc:bla:stanee:v:57:y:2003:i:1:p:136-157
    DOI: 10.1111/1467-9574.00225
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    Cited by:

    1. Banerjee, Moulinath & Mukherjee, Debasri & Mishra, Santosh, 2009. "Semiparametric binary regression models under shape constraints with an application to Indian schooling data," Journal of Econometrics, Elsevier, vol. 149(2), pages 101-117, April.
    2. Gwennaëlle Mabon, 2017. "Adaptive Deconvolution on the Non-negative Real Line," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 707-740, September.
    3. Carrasco, Marine & Florens, Jean-Pierre, 2011. "A Spectral Method For Deconvolving A Density," Econometric Theory, Cambridge University Press, vol. 27(3), pages 546-581, June.
    4. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, March.
    5. Holzmann, Hajo & Bissantz, Nicolai & Munk, Axel, 2007. "Density testing in a contaminated sample," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 57-75, January.
    6. Yatracos, Yannis G., 2018. "PLUG-IN L2-UPPER ERROR BOUNDS IN DECONVOLUTION, FOR A MIXING DENSITY ESTIMATE IN Rd AND FOR ITS DERIVATIVES," IRTG 1792 Discussion Papers 2018-061, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".

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