Classification and discrimination problems with applications, part I

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Abstract
This paper presents some of the results of the collaboration of the two authors, a mathematical‐statistician and a physical‐anthropologist, who have worked together since about 1960. Part I will consist of three chapters. Chapter I contains a description of the problems, especially concerning physical anthropology, which constitute the main motivation for this paper. Chapter 2 summarizes well‐known results which are included in order to make the paper self‐contained. Chapter 3 is mainly devoted to theunivariatetwo‐population classification problem and based on assumptions of normality and equality of the variances. Explicit expressions (Section 3.3) and confidence intervals (Section 3.4) arc obtained for the two misclassification probabilities of the maximum likelihood ruleφ* (Section 3.2) which is of application if the two kinds of error are equally bad. A Ncyman‐Pearson formulation is considered (Section 3.7). The asymptotic distribution is derived of an estimator for the posterior probability that the individual comes from Population 2 (Section 3.6). An interesting difficulty, frequently met with in physical anthropology, is that many individuals have to be classified without any (or with only small) reference samples being available from the relevant populations (Section 3.8). Part II will consist of two chapters. Chapter 4 contains new results formultivariateclassification and discrimination problems. Chapter 5 contains applications.

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