On unbiased optimal L-statistics quantile estimators
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.
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Volume (Year): 82 (2012)
Issue (Month): 11 ()
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- Davide Ferrari & Sandra Paterlini, 2007.
"The Maximum Lq-Likelihood Method: an Application to Extreme Quantile Estimation in Finance,"
Center for Economic Research (RECent)
001, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
- Davide Ferrari & Sandra Paterlini, 2007. "The Maximum Lq-Likelihood Method: an Application to Extreme Quantile Estimation in Finance," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 07071, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
- Davide Ferrari & Sandra Paterlini, 2007. "The Maximum Lq-Likelihood Method: an Application to Extreme Quantile Estimation in Finance," Department of Economics 555, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
- 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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