Asymptotic linear estimation of the quantile function of a location-scale Family of distributions based on selected order statistics

Abstract

Abstract. Some general asymptotic methods of estimating the quantile function, Q(~), 0 < ~ < 1, of location-scale fainilies of distributions based on a few selected order statistics are considered, with applications to some non-regular distributions. Specific results are discussed for the ABLUE of Q(~) for the location-scale exponential and double exponential distributions. As a further application of the exponential results, we discuss the asymptotically best optimal spacings for the location-scale logistic distribution.