Methods of estimation

Abstract

The practical man may entertain some misgivings about the methods discussed in the last two chapters. Bayesian point estimation appears to be very flexible, but if there is no secure basis for a particular prior distribution and only a sketchy idea of the loss function, is there not a danger of drawing misleading conclusions? As to the principle of best unbiased estimation, he might complain that sufficient statistics are sometimes excessively numerous or possess incomplete distributions (these last objections are illustrated in the following two examples). There is a clear demand for routine procedures, of wide applicability, which will (generally) produce unique estimators. Such estimators should, in some sense, be ‘good’. However, we might be prepared to sacrifice some degree of optimality in small samples, provided efficiency tended to be high in large samples. Two well-established routines are discussed in this chapter.