Showing papers by "Herman Chernoff published in 1973"

The Use of Faces to Represent Points in k- Dimensional Space Graphically

Abstract: A novel method of representing multivariate data is presented. Each point in k-dimensional space, k≤18, is represented by a cartoon of a face whose features, such as length of nose and curvature of mouth, correspond to components of the point. Thus every multivariate observation is visualized as a computer-drawn face. This presentation makes it easy for the human mind to grasp many of the essential regularities and irregularities present in the data. Other graphical representations are described briefly.

Approaches in Sequential Design of Experiments

Abstract: : Sequential design of experiments refers to problems of inference characterized by the fact that as data accumulate, the experimenter can choose whether or not to experiment further. If he decides to experiment further, he can decide which experiment to carry out next and if he decides to stop experimentation, he must decide what terminal decision to make. The literature contains two broad types of general approach and several major classes of applications. One general approach is that of stochastic approximation. Three variations are the Robbins-Monro methods, Box-Wilson response surface methods and the up-and-down methods. The other general approach consists of finding optimal or asymptotically optimal designs, generally in a Bayesian decision theoretic context. Special classes of applications include survey sampling, multilevel continuous sampling inspection, selecting the largest of k populations, which includes clinical trials and two-armed bandit-type problems, screening experiments, group testing, and search problems.

Some Measures for Discriminating between Normal Multivariate Distributions with Unequal Covariance Matrices

Abstract: : Suppose that a statistician is permitted access to data which are more precise under (H sub 1) than under (H sub 2) where each hypothesis specifies a multivariate normal distribution. He is also allowed a choice between additional data more precise under (H sub 1) than under (H sub 2) or data in which the reverse is true. In a previous paper it was shown that if a linear discriminant function is used there is a premium on selecting the additional data to be more precise under (H sub 1). In the paper this result is extended to the case where the likelihood-ratio test is used. The results involve several alternate measures for discriminating between normal multivariate distributions with unequal covariance matrices. (Author)