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Discriminant analys...
Discriminant analysis in small and large dimensions
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- Bodnar, Taras (author)
- Stockholms universitet,Matematiska institutionen,Department of Mathematics, Stockholm University
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- Mazur, Stepan, 1988- (author)
- Örebro universitet,Handelshögskolan vid Örebro Universitet,Unit of Statistics,School of Business, Örebro University
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- Ngailo, Edward, 1982- (author)
- Department of Mathematics, Stockholm University, Stockholm, Sweden,Department of Mathematics, University of Dar es Salaam, Tanzania
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- Parolya, Nestor (author)
- Institute of Empirical Economics, Leibniz University of Hannover, Hannover, Germany,Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands
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(creator_code:org_t)
- Providence, Rhode Island : American Mathematical Society (AMS), 2020
- 2020
- English.
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In: Theory of Probability and Mathematical Statistics. - Providence, Rhode Island : American Mathematical Society (AMS). - 1547-7363 .- 0094-9000. ; 100, s. 21-41
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Abstract
Subject headings
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- 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 mean vectors. A stochastic representation for the discriminant function coefficients is derived, which is then used 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 small and large dimensions. A stochastic representation is established, which allows to compute the error rate in an efficient way. We further compare the calculated error rate with the optimal one obtained under the assumption that the covariance matrix and the two mean vectors are known. Finally, we present 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- discriminant function
- stochastic representation
- large-dimensional asymp- totics
- random matrix theory
- classification analysis
Publication and Content Type
- ref (subject category)
- art (subject category)
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