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On the estimation of the quantile density function

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  • Falk, Michael

Abstract

Under fairly general conditions, asymptotic normality is achieved for the histogram type estimator of the underlying quantile density function as well as for a kernel type competitor. This entails the comparison of the asymptotic relative efficiencies of these estimators.

Suggested Citation

  • Falk, Michael, 1986. "On the estimation of the quantile density function," Statistics & Probability Letters, Elsevier, vol. 4(2), pages 69-73, March.
    • Handle: RePEc:eee:stapro:v:4:y:1986:i:2:p:69-73
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    Citations

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    Cited by:

    1. Cheng, Cheng, 1998. "A Berry-Esséen-type theorem of quantile density estimators," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 255-262, August.
    2. Dodge, Yadolah & Jurecková, Jana, 1995. "Estimation of quantile density function based on regression quantiles," Statistics & Probability Letters, Elsevier, vol. 23(1), pages 73-78, April.
    3. Pasha Andreyanov & Grigory Franguridi, 2021. "Nonparametric inference on counterfactuals in first-price auctions," Papers 2106.13856, arXiv.org, revised Jun 2022.
    4. Marc Hallin & Bas Werker, 2003. "Semiparametric efficiency, distribution-freeness, and invariance," ULB Institutional Repository 2013/2119, ULB -- Universite Libre de Bruxelles.
    5. Emad A. A. Aly & Marilou O. Hervas, 1999. "Nonparametric inference for Zenga's measure of income inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1-2), pages 69-84.
    6. Demet Batur & F. Fred Choobineh, 2021. "Selecting the Best Alternative Based on Its Quantile," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 657-671, May.
    7. Cheng, Cheng, 2002. "Almost-sure uniform error bounds of general smooth estimators of quantile density functions," Statistics & Probability Letters, Elsevier, vol. 59(2), pages 183-194, September.
    8. Hui Dong & Marvin K. Nakayama, 2017. "Quantile Estimation with Latin Hypercube Sampling," Operations Research, INFORMS, vol. 65(6), pages 1678-1695, December.
    9. Grabaskas, Dave & Nakayama, Marvin K. & Denning, Richard & Aldemir, Tunc, 2016. "Advantages of variance reduction techniques in establishing confidence intervals for quantiles," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 187-203.
    10. Michael Falk, 1997. "On Mad and Comedians," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(4), pages 615-644, December.
    11. Richard S.J. Tol, 2013. "Measuring catch-up growth in malnourished populations," Working Paper Series 6013, Department of Economics, University of Sussex Business School.
    12. Tol, Richard S.J., 2013. "Identifying excellent researchers: A new approach," Journal of Informetrics, Elsevier, vol. 7(4), pages 803-810.
    13. Arup Bose & Probal Chaudhuri, 1993. "On the dispersion of multivariate median," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 541-550, September.
    14. Futschik, A., 1999. "A new estimate of the mode based on the quantile density," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 145-152, June.

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