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Sampling strategy for optimal classification into one of two correlated normal populations. (English) Zbl 1440.62235

Summary: A unit \(\omega\) is to be classified into one of two correlated homoskedastic normal populations by linear discriminant function known as \(W\) classification statistic [T. W. Anderson, Ann. Stat. 1, 964–972 (1973; Zbl 0278.62009); An introduction to multivariate statistical analysis. 2nd ed. New York, NY: Wiley (1984; Zbl 0651.62041); G. J. MacLachlan, Discriminant analysis and statistical pattern recognition. New York, NY: Wiley (1992; Zbl 0850.62481)]. The two populations studied here are two different states of the same population, like two different states of a disease where the population is the population of diseased patient. When a sample unit is observed in both the states (populations), the observations made on it (which form a pair) become correlated. A training sample is unbalanced when not all sample units are observed in both the states. Paired and also unbalanced samples are natural in studies related to correlated populations. The authors [Calcutta Stat. Assoc. Bull. 54, No. 215–216, 167–179 (2003; Zbl 1057.62045)] studied the effect of unbalanced training sample structure on the performance of \(W\) statistics in the univariate correlated normal set-up for finding optimal sampling strategy for a better classification rate. In this study, the results are extended to the multivariate case with discussion on application in real scenario.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62D05 Sampling theory, sample surveys
62E20 Asymptotic distribution theory in statistics
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