Maximum probability estimators in the case of exponential distribution

Abstract

In 1966–1969L. Weiss andJ. Wolfowitz developed the theory of „maximum probability” estimators (m.p.e.'s). M.p.e.'s have the property of minimizing the limiting value of the risk (see (2.10).) In the present paper, therfore, after a short description of the new method, a fundamental loss function is introduced, for which—in the so-called regular case—the optimality property of the maximum probability estimators yields the classical result ofR.A. Fisher on the asymptotic efficiency of the maximum likelihood estimator. Thereby it turns out that the m.p.e.'s possess still another important optimality property for this loss function. For the latter the parameters of the exponential distribution—in the one-and the two-dimensional case—are estimated by the new method; for the estimation of the location parameter aWeibull distribution — in a more general sense — is taken as a basis. This shows that the maximum likelihood estimators involve a greater risk than the m.p.e.'s.