Assignment Methods in Combinatorial Data Analysis

Abstract

This monograph is extremely interesting because it integrates many classes of permutation techniques in a highly cohesive manner. Being confined to permutation methods, the techniques are strictly data dependent (i.e., all inferences depend only on the permutation structure associated with the available data). As a consequence, this monograph avoids the all-too-common practice involving the assumption of a totally unjustified distribution (e.g., a univariate or multivariate normal distribution) in applications of statistical methods that influences (perhaps overwhelms) any inference resulting from such methods. All the methods considered in this monograph depend on indices of merit that are called objective functions. A well-known example of an objective function is the Pearson correlation coefficient. In this perspective, the objective functions considered in this monograph are nothing more than univariate or multivariate variations and/or extensions of the Pearson correlation coefficient. The intuitive notion of proximity (closeness between objects) is a major consideration in the choice of an objective function. Because permutation methods involve random assignments, the statistical approaches of this monograph are termed assignment models. First, second, and higher order assignment models are considered. A general rth-order assignment model is based on an objective function given by

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