Linear Estimation of the Parameters of the Extreme-Value Distribution Based on Suitably Chosen Order Statistics

Best linear unbiased estimates (BLUEs) based on a few order statistics are found for the location and scale parameters of the extreme-value distribution (Type-I asymptotic distribution of smallest values), when one or both parameters are unknown, such that the estimates have maximum efficiencies among the BLUEs based on the same number of order statistics. These estimates are then compared with the BLUEs and asymptotically best linear estimates (ABLEs) based on a few order statistics whose ranks were determined from the spacings that maximize the asymptotic efficiencies of the ABLEs. An application to the Weibull distribution is given.