Approximation of misclassification probabilities using quadratic classifier for repeated measurements with known covariance matrices

Linköpings universitet, Tillämpad matematik Linköpings universitet, Tekniska fakulteten Department of Mathematics, University of Rwanda Department of Mathematics, University of Rwanda Department of Mathematics, University of Rwanda Linköing 2024

Quadratic discriminant analysis is a well-established supervised classification method, which extends the linear the linear discriminant analysis by relaxing the assumption of equal variances across classes. In this study, quadratic discriminant analysis is used to develop a quadratic classification rule based on repeated measurements. We employ a bilinear regression model to assign new observations to predefined populations and approximate the misclassification probability. Through weighted estimators, we estimate unknown mean parameters and derive moments of the quadratic classifier. We then conduct numerical simulations to compare misclassification probabilities using true and estimated mean parameters, as well as probabilities computed through simulation. Our findings suggest that as the distance between groups widens, the misclassification probability curve decreases, indicating that classifying observations is easier in widely separated groups compared to closely clustered ones.
This report has not been peer reviewed.

misclassification probability; repeated measurements; quadratic classifier; expectation; approximation.; Probability Theory and Statistics; Sannolikhetsteori och statistik; Report; info:eu-repo/semantics/report; text

10.3384.LiTH-MAT-R-2024-02

Open access content. Open access content
info:eu-repo/semantics/openAccess

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UPE oai:DiVA.org:liu-206138
0000-0001-9896-4438
doi:10.3384/LiTH-MAT-R-2024-02
1453488516

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