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EPMC estimation in discriminant analysis when the dimension and sample sizes are large. (English) Zbl 1365.62250

Summary: In this paper we obtain a higher order asymptotic unbiased estimator for the expected probability of misclassification (EPMC) of the linear discriminant function when both the dimension and the sample size are large. Moreover, we evaluate the mean squared error of our estimator. We also present a numerical comparison between the performance of our estimator and that of the other estimators based on M. Okamoto [Ann. Math. Stat. 34, 1286–1301 (1963; Zbl 0117.37101); ibid. 39, 1358 (1968; Zbl 0162.22502)] and Y. Fujikoshi and T. Seo [Random Oper. Stoch. Equ. 6, No. 3, 269–280 (1998; Zbl 0924.62070)]. It is shown that the bias and the mean squared error of our estimator are less than those of the other estimators.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62F12 Asymptotic properties of parametric estimators
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Full Text: Euclid