The Efficiency of a Linear Discriminant Function Based on Unclassified Initial Samples

Abstract

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Estimation of a discriminant function from a mixture of two inverse gaussian distributions when sample size is small

“…This measure of asymptotic relative efficiency was used by O'Nei11 (1978) and Ganesalingam and McLachlan (1978).…”

“…In all these studies the underlying populations are assumed to be normal. Cianesalingarn and McLachlan (1979) found from simulation cxperitnents that the mixture discriminant function performed satisfactorily although the maximum likelihood estimates of the parameters cstirnatcd from the mixed samplcs werc poor, O'Neill (1978) and Ganesalingam and McLachlan (1978) prcsent only asymptotic results.…”

A case-study on naïve labelling for the nearest mean and the linear discriminant classifiers

“…Note that Eq. (12) can be used to derive the optimal boundaries for any priors . Table 1 shows the Bayes error rate, the optimal boundaries b * and the error rates for the three distributions.…”

Mixture Models in View of Evidential Analysis

“…Following Rao's (1948) article likelihood estimation appears not to have been pursued further until Hasselblad (1966Hasselblad ( , 1969 addressed the problem, initially for a mixture of g univariate normal distributions with equal variances. The likelihood approach to the fitting of mixture models, in particular normal mixtures, has since been utilized by several authors, including Hosmer (1973aHosmer ( , 1973bHosmer ( , 1974Hosmer ( , 1978, O'neill (1978), and Ganesalingam and Mclachlan (1978, 1979, 1980. Butler (1986) noted that Jeffreys (1932) used essentially the Expectation-Maximization (EM) algorithm in iteratively computing the estimates of the means of two univariate normal population, which had known variances and which were mixed in known proportions.…”