Admissible, Minimax and Equivariant Estimators of Life Distributions from Type II Censored Samples

In life testing, the unique minimum variance unbiased estimator (MVUE) θ is often used when it exists. However it has been shown for certain distributions that an estimator of the form kθ with uniformly smaller mean square error exists. Such extimators are derived here for a class of life distributions and are shown to be admissible, minimax, and (in most cases) equivariant. The underlying distribution from which the samples are drawn follows a generalized life model (GLM) which includes a model proposed by Epstein & Sobel, Weibull, exponential, and Rayleigh distributions as special cases. Results are also given for the Type II asymptotic distribution of largest values, Pareto, and limited distributions. In addition, admissible linear estimators of the form aθ + b are obtained and it is shown that they are a form of locally best estimators for some portion of the parameter space. Both kθ and aθ + b could be used in nonrepetitive estimation problems where bias causes no difficulty.