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L1 Properties of the Nadaraya Quantile Estimator

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  • É. Youndjé

    (Université de Rouen Normandie)

Abstract

Let X be a real random variable having f as density function. Let F be its cumulative distribution function and Q its quantile function. For h > 0, let Fh and Qh denote respectively the Nadaraya kernel estimator of F and Q. In the first part of this paper the almost sure convergence of the conventional L1 distance between Qh and Q is established. In the second part, the L1 right inversion distance is introduced. The representation of this L1 right inversion distance in terms of Fh and F is given. This representation allows us to suggest ways to choose a global bandwidth for the estimator Qh.

Suggested Citation

  • É. Youndjé, 2022. "L1 Properties of the Nadaraya Quantile Estimator," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 867-884, August.
    • Handle: RePEc:spr:sankha:v:84:y:2022:i:2:d:10.1007_s13171-020-00225-0
    DOI: 10.1007/s13171-020-00225-0
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    References listed on IDEAS

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    1. Lejeune, Michel & Sarda, Pascal, 1992. "Smooth estimators of distribution and density functions," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 457-471, November.
    2. Cai, Zongwu & Roussas, George G., 1997. "Smooth estimate of quantiles under association," Statistics & Probability Letters, Elsevier, vol. 36(3), pages 275-287, December.
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