On using a loss function in selecting the best of two gamma populations in terms of their scale parameters

This paper continues the study of the subset selection procedure proposed by van der Laan and van Eeden (1993). In this 1993 paper the authors consider a location problem and base their procedure on a continuous loss function. This loss function takes into account the "distance", in parameter values, between the populations under consideration and the best one among the ones in the selected subset. In defining this "distance", they incorporate the notion of "epsilon-best" studied by, e.g., Desu (1970), Lam (1986), van der Laan (1992), Gill and Sharma (1993) and Gill, Sharma and Misra (1993). As an example of their results, van der Laan and van Eeden (1993) consider the case of two normal populations with equal known variances. The present paper develops a similar procedure for scale parameters. The case of two gamma populations with equal known shape parameters is studied in detail.