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Point estimation for the scale and location parameters of the extreme-value (Type I) distribution by linear functions of order statistics from Type II progressively censored samples is investigated. Four types of linear estimators are considered: the best linear unbiased (BLU), an approximation to the BLU, unweighted regression, and a linearized maximum likelihood. Linear transformations of the estimators are also considered for reducing mean square errors. Exact bias, variance, and mean square error comparisons of the estimators are made for several censoring patterns. Since the natural logarithms of Weibull variates have extreme-value distributions, the investigation is applicable to estimation for Weibull distributions.
Thomas et al. (1972) studied this question.