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Density estimation for data with rounding errors

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  • Wang, B.
  • Wertelecki, W.

Abstract

Rounding of data is common in practice. The problem of estimating the underlying density function based on data with rounding errors is addressed. A parametric maximum likelihood estimator and a nonparametric bootstrap kernel density estimator are proposed. Simulations indicate that the maximum likelihood approach performs well when prior information on the functional form of the underlying distribution is available, while the kernel-type estimator attains stable and good performance in various cases. The proposed methods are further applied to detect the distributional difference of head circumferences from two Chernobyl impacted regions of Ukraine.

Suggested Citation

  • Wang, B. & Wertelecki, W., 2013. "Density estimation for data with rounding errors," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 4-12.
    • Handle: RePEc:eee:csdana:v:65:y:2013:i:c:p:4-12
    DOI: 10.1016/j.csda.2012.02.016
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    References listed on IDEAS

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    1. Koo, Ja-Yong & Kooperberg, Charles, 2000. "Logspline density estimation for binned data," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 133-147, January.
    2. Ansley Coale & Shaomin Li, 1991. "The Effect of Age Misreporting in China on the Calculation of Mortality Rates at Very High Ages," Demography, Springer;Population Association of America (PAA), vol. 28(2), pages 293-301, May.
    3. Prithwis Gupta, 1975. "A general method of correction for age misreporting in census populations," Demography, Springer;Population Association of America (PAA), vol. 12(2), pages 303-312, May.
    4. A. Delaigle & I. Gijbels, 2004. "Bootstrap bandwidth selection in kernel density estimation from a contaminated sample," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 19-47, March.
    5. B. W. Silverman, 1982. "Kernel Density Estimation Using the Fast Fourier Transform," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(1), pages 93-99, March.
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    1. Christopher Withers & Saralees Nadarajah, 2015. "Cumulants of a random variable distributed uniformly on the first $$n$$ n integers," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(2), pages 229-236, April.
    2. Groß, Marcus & Rendtel, Ulrich & Schmid, Timo & Schmon, Sebastian & Tzavidis, Nikos, 2015. "Estimating the density of ethnic minorities and aged people in Berlin: Multivariate kernel density estimation applied to sensitive geo-referenced administrative data protected via measurement error," Discussion Papers 2015/7, Free University Berlin, School of Business & Economics.
    3. Christopher S. Withers & Saralees Nadarajah, 2015. "Bias reduction when data are rounded," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 236-271, August.
    4. Marcus Groß & Ulrich Rendtel & Timo Schmid & Sebastian Schmon & Nikos Tzavidis, 2017. "Estimating the density of ethnic minorities and aged people in Berlin: multivariate kernel density estimation applied to sensitive georeferenced administrative data protected via measurement error," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(1), pages 161-183, January.
    5. Walter, Paul & Weimer, Katja, 2018. "Estimating poverty and inequality indicators using interval censored income data from the German microcensus," Discussion Papers 2018/10, Free University Berlin, School of Business & Economics.
    6. Bermúdez, Lluís & Karlis, Dimitris & Santolino, Miguel, 2017. "A finite mixture of multiple discrete distributions for modelling heaped count data," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 14-23.

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