On The Optimality Of Some Subset Selection Procedures

On the Optimality of Some Subset Selection Procedures

As measures of goodness of a selection rule, usually two quantities, the probability of a correct selection and the expected size of the selected subset, are considered. Based on these two criteria, Gupta and Huang (1980) proved a theorem to derive a selection procedure with some optimality property. However, the theorem cannot be applied to the unequal sample sizes case. In this paper, its authors use a different method to generalize this theorem to the unequal sample sizes case. Also a dual problem is investigated. Also, they treat a selection procedure in terms of multiple tests. Based on this approach, an optimality result is derived. (Author).

On Optimal Subset Selection Procedures

Optimal Subset Selection

In the course of one's research, the expediency of meeting contractual and other externally imposed deadlines too often seems to take priority over what may be more significant research findings in the longer run. Such is the case with this volume which, despite our best intentions, has been put aside time and again since 1971 in favor of what seemed to be more urgent matters. Despite this delay, to our knowledge the principal research results and documentation presented here have not been superseded by other publications. The background of this endeavor may be of some historical interest, especially to those who agree that research is not a straightforward, mechanistic process whose outcome or even direction is known in ad vance. In the process of this brief recounting, we would like to express our gratitude to those individuals and organizations who facilitated and supported our efforts. We were introduced to the Beale, Kendall and Mann algorithm, the source of all our efforts, quite by chance. Professor Britton Harris suggested to me in April 1967 that I might like to attend a CEIR half-day seminar on optimal regression being given by Professor M. G. Kendall in Washington. D. C. I agreed that the topic seemed interesting and went along. Had it not been for Harris' suggestion and financial support, this work almost certainly would have never begun.