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A formulation is given and a procedure is proposed for constructing a confidence interval for a certain ordered (location or scale) parameter and for simultaneously selecting all populations having parameters equal or larger than this ordered parameter with a preassigned minimal probability. The well-known indifference-zone formulation of the ranking problem is obtained as a special case as is the problem of interval estimation of an ordered parameter., Prepared in cooperation with Nebraska Univ. Lincoln.

A procedure based on order statistics is given for the interval estimation of the largest alpha-quantile of several continuous distributions. Results on infimum of coverage probability are obtained for one-sided and two- sided intervals. An optimality criterion is proposed and an algorithm is given for two-sided intervals. Large sample approximations are also considered., Prepared in cooperation with Nebraska Univ., Lincoln.

A graphical method of representing multivariate data consists of having a computer draw a cartoon of a face which is determined by 18 parameters (features) including length of nose, curvature of mouth, slant of eyes, length of eyes, etc. If a sample of 8-dimensional vector observations is presented each component of a vector can be made to determine one of the 18 features and 10 constants can be selected for the remaining features. The resulting output is a series of faces, one for each 8 dimensional observation, which can be studied visually. An experiment was designed to evaluate the effect of a random permutation of the features on the visual ability to classify observations from two multivariate populations into two separate groups corresponding to the original populations. It is estimated that a random permutation may affect the error rate in this classification task by about 25%. (Author), Prepared in cooperation with Sir George Williams Univ., Montreal (Quebec).

The paper considers the problem of selection of t largest from among k multiple correlation coefficients, each arising from one of k independent p-variate normal populations with unknown mean vectors and unknown covariance matrices. A selection procedure based on a natural ordering of the squared sample multiple correlation coefficients is proposed and the infimum of the probability of a correct selection over a specified preference zone in the parameter space is evaluated for large values of the common sample size n. A table giving values of n for preassigned minimal probability of a correct selection is appended. Certain decision-theoretic properties of the proposed procedure and some applications, especially the case of the simple correlation coefficients arising in bivariate normal populations, are discussed. (Author)

The paper is concerned with certain multiple-decision procedures based on ranks which have been proposed for analyzing data in a one-way layout: X sub ij = theta sub i + epsilon sub ij, i = 1,...,k, j =1,...,n where the errors (epsilon sub ij) are independent, have the same known cumulative distribution function (cdf) F and where theta = (theta sub 1,...,theta sub k) is unknown. Two problems are considered: (1) Select the indices of the t largest theta-values. (2) Select a subset containing the index of the largest theta-value. (Author), Prepared in cooperation with Ohio State Univ., Columbus, contract NASA-NGR36-008-040.

A decision maker is confronted with k populations pi sub 1,...,pi sub k (say, k lots of items available for purchase) and a control population pi sub o and must, on the basis of random samples of common size from pi sub o,...,pi sub k, select those which are at least as good as pi sub o. A nonparametric procedure R based on order statistics is proposed as a solution for this problem; R guarantees with a preassigned probability P* that, when each pi sub i is stochastically ordered with respect to pi sub o, all populations better than pi sub o will be selected., See also Technical report 132, AD-661 251.