ABSTRACT
We reconsider the general Stein-type two-stage methodology of Mukhopadhyay and Duggan (1999) which had incorporated partial information in the form of a known and positive lower bound for the otherwise unknown nuisance parameter. This revised methodology was shown to enjoy customary second-order properties and expansions for functions of the associated stopping variable, under appropriate conditions. In this paper, new machineries are provided which help one to obtain the third-order and higher than third-order expansions of the analogous functions of the associated stopping variable, under appropriate conditions. These general techniques are then applied in a variety of estimation as well as selection and ranking problems.
