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An Investigation of Quantile Function Estimators Relative to Quantile Confidence Interval Coverage

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  • Lai Wei
  • Dongliang Wang
  • Alan D. Hutson

Abstract

In this article, we investigate the limitations of traditional quantile function estimators and introduce a new class of quantile function estimators, namely, the semi-parametric tail-extrapolated quantile estimators, which has excellent performance for estimating the extreme tails with finite sample sizes. The smoothed bootstrap and direct density estimation via the characteristic function methods are developed for the estimation of confidence intervals. Through a comprehensive simulation study to compare the confidence interval estimations of various quantile estimators, we discuss the preferred quantile estimator in conjunction with the confidence interval estimation method to use under different circumstances. Data examples are given to illustrate the superiority of the semi-parametric tail-extrapolated quantile estimators. The new class of quantile estimators is obtained by slight modification of traditional quantile estimators, and therefore, should be specifically appealing to researchers in estimating the extreme tails.

Suggested Citation

  • Lai Wei & Dongliang Wang & Alan D. Hutson, 2015. "An Investigation of Quantile Function Estimators Relative to Quantile Confidence Interval Coverage," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(10), pages 2107-2135, May.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:10:p:2107-2135
    DOI: 10.1080/03610926.2013.775304
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    Cited by:

    1. Guo, Yating & Wong, Wing-Keung & Su, Nan & Ghardallou, Wafa & Orosco Gavilán, Juan Carlos & Uyen, Pham Thi Minh & Cong, Phan The, 2023. "Resource curse hypothesis and economic growth: A global analysis using bootstrapped panel quantile regression analysis," Resources Policy, Elsevier, vol. 85(PA).
    2. Yogendra P. Chaubey & Isha Dewan & Jun Li, 2021. "On Some Smooth Estimators of the Quantile Function for a Stationary Associated Process," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 114-139, May.

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