L1 Properties of the Nadaraya Quantile Estimator

É. Youndjé ()
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É. Youndjé: Université de Rouen Normandie

Sankhya A: The Indian Journal of Statistics, 2022, vol. 84, issue 2, No 18, 867-884

Abstract: 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.

Keywords: Quantile function; Quantile estimation; Kernel estimation; Bandwidth selection; Primary 62G05; Secondary 62G99 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13171-020-00225-0

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