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Generalization of normal discriminant analysis using fourier series density estimators
Author(s) -
OdomMaryon Tamara,
Langholz Bryan,
Niland Joyce,
Azen Stanley
Publication year - 1991
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4780100319
Subject(s) - linear discriminant analysis , univariate , mathematics , estimator , normality , generalization , series (stratigraphy) , statistics , quadratic classifier , multivariate normal distribution , discriminant , optimal discriminant analysis , multivariate statistics , kernel fisher discriminant analysis , normal distribution , fourier series , pattern recognition (psychology) , artificial intelligence , computer science , support vector machine , mathematical analysis , paleontology , facial recognition system , biology
In this paper we examine the efficiency of a generalization of the traditional normal linear (LDA) or quadratic (QDA) discriminant analysis. This procedure (the generalized discriminant analysis, GDA) replaces each normal density used in the traditional classification rule by a Fourier series density estimator which ‘adjusts’ the normal density if the data deviate markedly from normality (for example, heavily skewed or multimodal). We derive the GDA in both the univariate and multivariate situations. In a simulation study for the univariate situation, we evaluate the relative efficiency of the GDA. In addition, we demonstrate the performance of the GDA through a series of multivariate applications. We conclude that if the distributions of the data do not deviate markedly from normality, the GDA is as efficient as the LDA or QDA. On the other hand, if either of the distributions deviates from normality, then the GDA, which performs as a semiparametric discriminant procedure, is more efficient than the LDA or QDA.