Piecewise Linear Continuous Estimators of the Quantile Function

Delphine Blanke () and Denis Bosq ()
Additional contact information
Delphine Blanke: Laboratoire de Mathématiques d’Avignon, LMA, Avignon Université
Denis Bosq: Laboratoire de Probabilités, Statistique et Modélisation, LPSM, CNRS, Sorbonne Universités

A chapter in Advances in Contemporary Statistics and Econometrics, 2021, pp 161-175 from Springer

Abstract: Abstract In Blanke and Bosq (2018), families of piecewise linear estimators of the distribution function F were introduced. It was shown that they reduce the mean integrated squared error (MISE) of the empirical distribution function $$F_n$$ F n and that the minimal MISE was reached by connecting the midpoints $$(\frac{X_k^{*}+ X^{*}_{k+1}}{2}, \frac{k}{n})$$ ( X k ∗ + X k + 1 ∗ 2 , k n ) , with $$X_1^{*},\dotsc ,X_n^{*}$$ X 1 ∗ , ⋯ , X n ∗ the order statistics. In this contribution, we consider the reciprocal estimators, built respectively for known and unknown support of distribution, for estimating the quantile function $$F^{-1}$$ F - 1 . We prove that these piecewise linear continuous estimators again strictly improve the MISE of the classical sample quantile function $$F_n^{-1}$$ F n - 1 .

Date: 2021
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-73249-3_9

Ordering information: This item can be ordered from
http://www.springer.com/9783030732493

DOI: 10.1007/978-3-030-73249-3_9

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().