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November 2020 Computable error bounds for asymptotic approximations of the quadratic discriminant function
Yasunori Fujikoshi
Hiroshima Math. J. 50(3): 313-324 (November 2020). DOI: 10.32917/hmj/1607396491

Abstract

This paper is concerned with computable error bounds for asymptotic approximations of the expected probabilities of misclassification (EPMC) of the quadratic discriminant function $Q$. A location and scale mixture expression for $Q$ is given as a special case of a general discriminant function including the linear and quadratic discriminant functions. Using the result, we provide computable error bounds for asymptotic approximations of the EPMC of $Q$ when both the sample size and the dimensionality are large. The bounds are numerically explored. Similar results are given for a quadratic discriminant function $Q_0$ when the covariance matrix is known.

Funding Statement

The author is supported by Grant-in-aid for Science Research (C), 16K00047, 2016–2018.

Citation

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Yasunori Fujikoshi. "Computable error bounds for asymptotic approximations of the quadratic discriminant function." Hiroshima Math. J. 50 (3) 313 - 324, November 2020. https://doi.org/10.32917/hmj/1607396491

Information

Received: 6 June 2019; Revised: 2 April 2020; Published: November 2020
First available in Project Euclid: 8 December 2020

MathSciNet: MR4184263
Digital Object Identifier: 10.32917/hmj/1607396491

Subjects:
Primary: 62H30
Secondary: 62E12

Rights: Copyright © 2020 Hiroshima University, Mathematics Program

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Vol.50 • No. 3 • November 2020
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