Discriminant analysis in small and large dimensions

T. Bodnar, S. Mazur, E. Ngailo, N. Parolya

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Abstract

We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different meanvectors. A stochastic representation for the discriminant function coefficients is derived, which is thenused to obtain their asymptotic distribution under the high-dimensional asymptotic regime. We investigate the performance of the classification analysis based on the discriminant function in both smalland large dimensions. A stochastic representation is established, which allows to compute the errorrate in an efficient way. We further compare the calculated error rate with the optimal one obtainedunder the assumption that the covariance matrix and the two mean vectors are known. Finally, wepresent an analytical expression of the error rate calculated in the high-dimensional asymptotic regime.The finite-sample properties of the derived theoretical results are assessed via an extensive Monte Carlo study.
Original languageEnglish
Pages (from-to)24-42
Number of pages19
JournalTheory of Probability and Mathematical Statistics
Volume100
DOIs
Publication statusE-pub ahead of print - 2019

Keywords

  • Discriminant function
  • stochastic representation
  • large-dimensional asymptotics
  • random matrix theory
  • classification analysis

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