A Comparison of Linear, Quadratic and Kernel Discriminant Rules for ECD Distributions Via ROC Analysis

FORBELSKÁ, Marie. A Comparison of Linear, Quadratic and Kernel Discriminant Rules for ECD Distributions Via ROC Analysis. In TIES 2007, 18th annual meeting of the International Environmetrics Society. First edition. Brno: Ivana Horová, Jiří Hřebíček, 2007, s. 40-40. ISBN 978-80-210-4333-6.

Základní údaje

Originální název

A Comparison of Linear, Quadratic and Kernel Discriminant Rules for ECD Distributions Via ROC Analysis

Název česky

Porovnání lineárních, kvadratických a jádrových diskriminačních pravidel pro ECD rozdělení s využitím ROC analýzy

Autoři

FORBELSKÁ, Marie

Vydání

First edition. Brno, TIES 2007, 18th annual meeting of the International Environmetrics Society, od s. 40-40, 1 s. 2007

Nakladatel

Ivana Horová, Jiří Hřebíček

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Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10103 Statistics and probability

Stát vydavatele

Česká republika

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Kód RIV

RIV/00216224:14310/07:00032275

Organizační jednotka

Přírodovědecká fakulta

ISBN

978-80-210-4333-6

Klíčová slova anglicky

parametric and nonparametric and semiparametric discriminant analysis; kernel density estimation; product kernels; bandwidth choice; boundary kernels; variable bandwidth selector; elliptically contoured distribution; ROC analysis

Štítky

bandwidth choice, boundary kernels, Elliptically contoured distribution, kernel density estimation, product kernels, ROC analysis, variable bandwidth selector

Příznaky

Mezinárodní význam, Recenzováno

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Anotace

V originále

The main approaches to discriminant analysis is considered with respect to the use of parametric models (based on the multivariate normal and elliptically contoured distributions), nonparametric models (based on the multivariate product Gaussian and polynomial kernels with various data-driven choices of the bandwidth) and also semiparametric models (based on the various kernel estimators for density functions of squared Mahalanobis distances). This paper demonstrates that linear and quadratic discriminant decision rules of classifying observation as coming from one of several multivariate normal distribution can be construct for much broader classes of distribution such as elliptical contoured distributions. While being much richer than the class of Gaussian distributions, the family of elliptically contoured distributions (ECD) inherits many of its attractive properties. This family includes as particular cases the following distributions: the normal, the t-Student, the Pearson type II and VII, the Kotz type, the logistic, the Laplace (also so-called double exponential), the contaminated normal, among many others. In the paper the attention is also focused to the applications of nonparametric and semiparametric discriminant methods (based on the kernel smoothing). The performance of a binary (two-groups) classifier with continuous output is often evaluated with receiver operating characteristic (ROC) curve analysis, which yields indices of accuracy such as the area under the curve (AUC). Various methodologies for estimating and comparing ROC curves have been developed. The most common method of ROC analysis is based on the bi-normal model. In this paper the attention is also concerned with a more general fully parameterized bi-distributional model assuming ECDs (bi-ECD model). Various nonparametric and semiparametric approaches are compared with classical parametric one by some real data via ROC curve analysis.

Česky

The main approaches to discriminant analysis is considered with respect to the use of parametric models (based on the multivariate normal and elliptically contoured distributions), nonparametric models (based on the multivariate product Gaussian and polynomial kernels with various data-driven choices of the bandwidth) and also semiparametric models (based on the various kernel estimators for density functions of squared Mahalanobis distances). This paper demonstrates that linear and quadratic discriminant decision rules of classifying observation as coming from one of several multivariate normal distribution can be construct for much broader classes of distribution such as elliptical contoured distributions. While being much richer than the class of Gaussian distributions, the family of elliptically contoured distributions (ECD) inherits many of its attractive properties. This family includes as particular cases the following distributions: the normal, the t-Student, the Pearson type II and VII, the Kotz type, the logistic, the Laplace (also so-called double exponential), the contaminated normal, among many others. In the paper the attention is also focused to the applications of nonparametric and semiparametric discriminant methods (based on the kernel smoothing). The performance of a binary (two-groups) classifier with continuous output is often evaluated with receiver operating characteristic (ROC) curve analysis, which yields indices of accuracy such as the area under the curve (AUC). Various methodologies for estimating and comparing ROC curves have been developed. The most common method of ROC analysis is based on the bi-normal model. In this paper the attention is also concerned with a more general fully parameterized bi-distributional model assuming ECDs (bi-ECD model). Various nonparametric and semiparametric approaches are compared with classical parametric one by some real data via ROC curve analysis.