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On unbiased optimal L-statistics quantile estimators

Author

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  • Li, Ling-Wei
  • Lee, Loo-Hay
  • Chen, Chun-Hung
  • Guo, Bo

Abstract

Recently, Li et al. (2012a,b) have presented two biased Optimal L-statistics Quantile Estimators (OLQEs). In this work, we present two unbiased versions of the two biased OLQEs. Similar to the biased OLQEs, the proposed unbiased OLQEs are able to accommodate a set of scaled populations and a set of location-scale populations, respectively. Furthermore, we compare the proposed unbiased OLQEs with two state-of-the-art efficient unbiased estimators, called Best Linear Unbiased Estimators (BLUEs). Although OLQEs and BLUEs have different aims and models, we point out that the two proposed unbiased OLQEs are closely related to the two BLUEs, respectively. The differences between the unbiased OLQEs and the BLUEs are also provided. We conduct an experimental study to demonstrate that, for a set of location-scale populations and extreme quantiles, if the main concern is large biases, then a proposed unbiased location equivariance OLQE is more appealing.

Suggested Citation

  • Li, Ling-Wei & Lee, Loo-Hay & Chen, Chun-Hung & Guo, Bo, 2012. "On unbiased optimal L-statistics quantile estimators," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1891-1897.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1891-1897
    DOI: 10.1016/j.spl.2012.05.027
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    References listed on IDEAS

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    1. Davide Ferrari & Sandra Paterlini, 2009. "The Maximum Lq-Likelihood Method: An Application to Extreme Quantile Estimation in Finance," Methodology and Computing in Applied Probability, Springer, vol. 11(1), pages 3-19, March.
    2. Balakrishnan, N. & Saleh, H.M., 2011. "Relations for moments of progressively Type-II censored order statistics from half-logistic distribution with applications to inference," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2775-2792, October.
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    2. Abrell, Jan & Rausch, Sebastian, 2016. "Cross-country electricity trade, renewable energy and European transmission infrastructure policy," Journal of Environmental Economics and Management, Elsevier, vol. 79(C), pages 87-113.
    3. Fadaeenejad, M. & Radzi, M.A.M. & AbKadir, M.Z.A. & Hizam, H., 2014. "Assessment of hybrid renewable power sources for rural electrification in Malaysia," Renewable and Sustainable Energy Reviews, Elsevier, vol. 30(C), pages 299-305.
    4. Fang, Xiande & Li, Dingkun, 2013. "Solar photovoltaic and thermal technology and applications in China," Renewable and Sustainable Energy Reviews, Elsevier, vol. 23(C), pages 330-340.

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