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Finite sample performance of deconvolving density estimators

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  • Wand, M. P.

Abstract

Recent studies have shown that the asymptotic performance of nonparametric curve estimators in the presence of measurement error will often be very much inferior to that when the observations are error-free. For example, deconvolution of Gaussian measurement error worsens the usual algebraic convergence rates of kernel estimators to very slow logarithmic rates. However, the slow convergence rates mean that very large sample sizes may be required for the asymptotics to take effect, so the finite sample properties of the estimator may not be very well described by the asymptotics. In this article finite sample calculations are performed for the important cases of Gaussian and Laplacian measurement error which provide insight into the feasibility of deconvolving density estimators for practical sample sizes. Our results indicate that for lower levels of measurement error deconvolving density estimators can perform well for reasonable sample sizes.

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  • Wand, M. P., 1998. "Finite sample performance of deconvolving density estimators," Statistics & Probability Letters, Elsevier, vol. 37(2), pages 131-139, February.
    • Handle: RePEc:eee:stapro:v:37:y:1998:i:2:p:131-139
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    1. Stefanski, Leonard A., 1990. "Rates of convergence of some estimators in a class of deconvolution problems," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 229-235, March.
    2. Wand, M. P., 1992. "Finite sample performance of density estimators under moving average dependence," Statistics & Probability Letters, Elsevier, vol. 13(2), pages 109-115, January.
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    Cited by:

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    3. Hongwen Guo & Sandip Sinharay, 2011. "Nonparametric Item Response Curve Estimation With Correction for Measurement Error," Journal of Educational and Behavioral Statistics, , vol. 36(6), pages 755-778, December.
    4. Ali Al-Sharadqah & Majid Mojirsheibani & William Pouliot, 2020. "On the performance of weighted bootstrapped kernel deconvolution density estimators," Statistical Papers, Springer, vol. 61(4), pages 1773-1798, August.
    5. Julie McIntyre & Leonard Stefanski, 2011. "Density Estimation with Replicate Heteroscedastic Measurements," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 81-99, February.
    6. Yousri Slaoui, 2021. "Data-driven Deconvolution Recursive Kernel Density Estimators Defined by Stochastic Approximation Method," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 312-352, February.
    7. 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.
    8. Zhang Saijuan & Krebs-Smith Susan M. & Midthune Douglas & Perez Adriana & Buckman Dennis W. & Kipnis Victor & Freedman Laurence S. & Dodd Kevin W. & Carroll Raymond J, 2011. "Fitting a Bivariate Measurement Error Model for Episodically Consumed Dietary Components," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-32, January.
    9. Isabel Proenca, 2005. "A Simple Deconvolving Kernel Density Estimator when Noise is Gaussian," Econometrics 0508006, University Library of Munich, Germany.
    10. Delaigle, Aurore & Hall, Peter, 2006. "On optimal kernel choice for deconvolution," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1594-1602, September.
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