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Estimating smooth distribution function in the presence of heteroscedastic measurement errors

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  • Wang, Xiao-Feng
  • Fan, Zhaozhi
  • Wang, Bin

Abstract

Measurement error occurs in many biomedical fields. The challenges arise when errors are heteroscedastic since we literally have only one observation for each error distribution. This paper concerns the estimation of smooth distribution function when data are contaminated with heteroscedastic errors. We study two types of methods to recover the unknown distribution function: a Fourier-type deconvolution method and a simulation extrapolation (SIMEX) method. The asymptotics of the two estimators are explored and the asymptotic pointwise confidence bands of the SIMEX estimator are obtained. The finite sample performances of the two estimators are evaluated through a simulation study. Finally, we illustrate the methods with medical rehabilitation data from a neuro-muscular electrical stimulation experiment.

Suggested Citation

  • Wang, Xiao-Feng & Fan, Zhaozhi & Wang, Bin, 2010. "Estimating smooth distribution function in the presence of heteroscedastic measurement errors," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 25-36, January.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:1:p:25-36
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    1. Delaigle, A. & Gijbels, I., 2004. "Practical bandwidth selection in deconvolution kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 249-267, March.
    2. Nicolai Bissantz & Lutz Dümbgen & Hajo Holzmann & Axel Munk, 2007. "Non‐parametric confidence bands in deconvolution density estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 483-506, June.
    3. Carriquiry, Alicia L. & Fuller, Wayne A., 1996. "A Semiparametric Approach to Estimating Usual Intake Distributions," Staff General Research Papers Archive 1036, Iowa State University, Department of Economics.
    4. Bissantz, Nicolai & Dümbgen, Lutz & Holzmann, Hajo & Munk, Axel, 2007. "Nonparametric confidence bands in deconvolution density estimation," Technical Reports 2007,03, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    5. Staudenmayer, John & Ruppert, David & Buonaccorsi, John P., 2008. "Density Estimation in the Presence of Heteroscedastic Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 726-736, June.
    6. John Staudenmayer & David Ruppert, 2004. "Local polynomial regression and simulation–extrapolation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 17-30, February.
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    3. Jochmans, Koen & Weidner, Martin, 2024. "Inference On A Distribution From Noisy Draws," Econometric Theory, Cambridge University Press, vol. 40(1), pages 60-97, February.
    4. Battistin, Erich & Lamarche, Carlos & Rettore, Enrico, 2020. "Quantiles of the Gain Distribution of an Early Child Intervention," CEPR Discussion Papers 14721, C.E.P.R. Discussion Papers.
    5. Wang, Xiao-Feng & Ye, Deping, 2015. "Conditional density estimation in measurement error problems," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 38-50.
    6. Bin Wang & Shu-Guang Zhang & Xiao-Feng Wang & Ming Tan & Yaguang Xi, 2012. "Testing for Differentially-Expressed MicroRNAs with Errors-in-Variables Nonparametric Regression," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-12, May.

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