EPMC estimation in discriminant analysis when the dimension and sample sizes are large
| Autor: | Hirofumi Wakaki, Tomoyuki Nakagawa, Tetsuji Tonda |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
High dimensional
Multiple discriminant analysis Algebra and Number Theory Mean squared error Estimator Asymptotic expansion Classification Linear discriminant analysis Discriminant analysis Expected probability of misclassification Dimension (vector space) Bias of an estimator Sample size determination Optimal discriminant analysis Statistics Geometry and Topology 62F12 62H30 Analysis Mathematics |
| Zdroj: | Hiroshima Math. J. 47, no. 1 (2017), 43-62 |
| ISSN: | 0018-2079 |
| DOI: | 10.32917/hmj/1492048847 |
| Popis: | 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 Okamoto (1963, 1968) and Fujikoshi and Seo (1998). It is shown that the bias and the mean squared error of our estimator are less than those of the other estimators. |
| Databáze: | OpenAIRE |
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