Scandinavian Working Papers in Economics

Working Papers,
Örebro University, School of Business

No 2017:6: Discriminant analysis in small and large dimensions

Taras Bodnar (), Stepan Mazur (), Edward Ngailo () and Nestor Parolya ()
Additional contact information
Taras Bodnar: Stockholm University, Postal: Department of Mathematics, Stockholm University , SE-10691 Stockholm, Sweden
Stepan Mazur: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden
Edward Ngailo: Stockholm University, Postal: Department of Mathematics, Stockholm University , SE-10691 Stockholm, Sweden
Nestor Parolya: University of Hannover, Postal: Institute of Empirical Economics, Leibniz University of Hannover, D-30167 Hannover, Germany

Abstract: In this article we study the distributional properties of the linear discriminant function under the assumption of the normality by comparing two groups with the same covariance matrix but di erent mean vectors. A stochastic representation of the discriminant function coecient is derived which is then used to establish the asymptotic distribution under the high-dimensional asymptotic regime. Moreover, we investigate the classi cation analysis based on the discriminant function in both small and large dimensions. In the numerical study, a good nite-sample perfor- mance of the derived large-dimensional asymptotic distributions is documented.

Keywords: discriminant function; stochastic representation; large-dimensional asymptotics; random matrix theory; classication analysis

JEL-codes: C12; C13; C44

27 pages, August 22, 2017

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