C337. Misspecified location and scale. 11. independence of and s2

A hierarchical Bayesian approach to the problem of estimating the largest normal mean is considered. Calculation of the posterior mean and the posterior variance involves, at worst, 3-dimensional numerical integration, for which an efficient Monte Carlo method of evaluation is given. An example is presented to illustrate the methodology. In the two populations case, computation of the posterior estimates can be substantially simplified and in special cases can actually be performed using closed form solutions. A simulation study has been done to compare mean square errors of some hierarchical Bayesian estimators that are expressed in closed forms and several existing estimators of the larger mean.     

Krishnaiah,P.R. and C.R. Rao (eds):Sampling. Handbook of Statistics,vol. 6

In a recent paper Yager (1988) introduced a special type of aggregation operators which he called OWA-operators and applied it to multicriteria decisionmaking. In our paper we give a more general definition of such operators and investigate in some detail the structural properties of them. In particular we introduce a well motivated ordering relation on weight systems which is different but compatible with Yager's degree of “orness”. Our results have immediate applications to the theory of generalized quantifiers as also discussed by Yager. Details concerning this topic will appear in a future paper.     

Jerome H. Friedman and Nicholas I. Fisher

Many data analytic questions can be formulated as (noisy) optimization problems. They explicitly or implicitly involve finding simultaneous combinations of values for a set of (input) variables that imply unusually large (or small) values of another designated (output) variable. Specifically, one seeks a set of subregions of the input variable space within which the value of the output variable is considerably larger (or smaller) than its average value over the entire input domain. In addition it is usually desired that these regions be describable in an interpretable form involving simple statements (rules) concerning the input values. This paper presents a procedure directed towards this goal based on the notion of patient rule induction. This patient strategy is contrasted with the greedy ones used by most rule induction methods, and semi-greedy ones used by some partitioning tree techniques such as CART. Applications involving scientific and commercial data bases are presented.