A simple comparision of mixture vs. nonanticipating estimation

When a problem entails an unknown nuisance parameter, estimating the parameter and (alternatively) integrating it out (with respect to some probability measure) are two of the approaches commonly used. Robbins and Siegmund (1973) proposed a non-anticipating estimation approach for problems which possess an intrinsic martingale structure which would be destroyed by the use of standard estimators. Here we compare this to the mixture (integration) approach in a sequential hypothesis testing context. We find that (in this context) the mixture is slightly better.