Bias in estimation from type 1 censored samples.

Let P be a family of probability distributions on R 1. This paper raises the question whether a parameter Q=Q (p), P=P, is estimate on the basis of a type 1 censored sample (i.e. censored on a fixed set C). Two theorems are given that state conditions on Q and C that ensure that Q is not estimable. The results are applied to estimation problems for the normal and POISSON distributions; it turns out that unbiased estimation is impossible in the majortty of practical cases.