ON THE EXISTENCE OF UNBIASED MONTE-CARLO ESTIMATORS

For many typical instances where Monte Carlo methods are applied attem pts were made to find unbiased estimators, since for them the Monte Ca rlo error reduces to the statistical error. These problems usually tak e values in the scalar field. If we study vector valued Monte Carlo me thods, then we are confronted with the question of whether there can e xist unbiased estimators. This problem is apparently new. Below it is settled precisely. Partial answers are given, indicating relations to several classes of linear operators in Banach spaces. (C) 1996 Academi c Press, Inc.