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Discriminant analysis in small and large dimensions

Taras Bodnar (), Stepan Mazur (), Edward Ngailo () and Nestor Parolya
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Taras Bodnar: Stockholm University, Postal: Department of Mathematics, Stockholm University , SE-10691 Stockholm, Sweden, http://www.su.se/profiles/tbodn-1.219689
Stepan Mazur: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden, https://www.oru.se/personal/stepan_mazur
Edward Ngailo: Stockholm University, Postal: Department of Mathematics, Stockholm University , SE-10691 Stockholm, Sweden

No 2017:6, Working Papers from Örebro University, School of Business

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 (search for similar items in EconPapers)
JEL-codes: C12 C13 C44 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ore
Date: 2017-08-22
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