On unbiased optimal LL-statistics quantile estimators

Recently, Li et al., 2012a and Li et al., 2012b have presented two biased Optimal LL-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.