ℒ1-deficiency of the sample quantile estimator with respect to a kernel quantile estimator

Mu Zhao; Hongmei Jiang; Yong Zhou

doi:10.1016/j.spl.2013.06.035

_ℒ1-deficiency of the sample quantile estimator with respect to a kernel quantile estimator

Mu Zhao, Hongmei Jiang^*, Yong Zhou

^*Corresponding author for this work

Statistics and Data Science

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The performance of the sample quantile estimator versus a kernel quantile estimator under the criterion of mean integrated absolute error (MIAE) for randomly right-censored data is considered in this paper. We show that the so called _ℒ1-deficiency of the sample quantile estimator with respect to the kernel quantile estimator is convergent to infinity. The optimal bandwidth in the sense of MIAE is obtained. Some simulation studies and one real data analysis are used to illustrate the results.

Original language	English (US)
Pages (from-to)	2399-2406
Number of pages	8
Journal	Statistics and Probability Letters
Volume	83
Issue number	10
DOIs	https://doi.org/10.1016/j.spl.2013.06.035
State	Published - Oct 2013

Keywords

-deficiency
Kernel quantile estimator
Optimal bandwidth
Sample quantile estimator

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1016/j.spl.2013.06.035

Cite this

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title = "ℒ1-deficiency of the sample quantile estimator with respect to a kernel quantile estimator",

abstract = "The performance of the sample quantile estimator versus a kernel quantile estimator under the criterion of mean integrated absolute error (MIAE) for randomly right-censored data is considered in this paper. We show that the so called ℒ1-deficiency of the sample quantile estimator with respect to the kernel quantile estimator is convergent to infinity. The optimal bandwidth in the sense of MIAE is obtained. Some simulation studies and one real data analysis are used to illustrate the results.",

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note = "Funding Information: The authors are very grateful to the Co-Editor-in-Chief Hira Koul, and an anonymous referee for their valuable and constructive comments. This work was partially supported by NSF Grant DMS-1043080 and NNSF of China (Grant No. 11171001 ). ",

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AU - Zhou, Yong

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AB - The performance of the sample quantile estimator versus a kernel quantile estimator under the criterion of mean integrated absolute error (MIAE) for randomly right-censored data is considered in this paper. We show that the so called ℒ1-deficiency of the sample quantile estimator with respect to the kernel quantile estimator is convergent to infinity. The optimal bandwidth in the sense of MIAE is obtained. Some simulation studies and one real data analysis are used to illustrate the results.

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