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Piecewise linear continuous estimators of the quantile function

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 $F_n$ and that the minimal MISE was reached by connecting the midpoints $(\frac{X_k^{\ast}+ X^{\ast}_{k+1}}{2}, \frac{k}{n})$, with $X_1^{\ast},\dotsc,X_n^{\ast}$ 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 $F^{-1}$. We prove that these piecewise linear continuous estimators again strictly improve the MISE of the classical sample quantile function $F_n^{-1}$.
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Contributor : Delphine Blanke Connect in order to contact the contributor
Submitted on : Wednesday, August 19, 2020 - 12:12:46 PM
Last modification on : Friday, August 5, 2022 - 3:00:08 PM
Long-term archiving on: : Monday, November 30, 2020 - 9:39:41 PM


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  • HAL Id : hal-02917464, version 1


Delphine Blanke, Denis Bosq. Piecewise linear continuous estimators of the quantile function. Advances in Contemporary Statistics and Econometrics, 2021, Festschrift in Honor of Christine Thomas-Agnan. ⟨hal-02917464⟩



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