A classification procedure using the multiple Fourier series

DOI10.1016/0020-0255(82)90036-6zbMath0535.62052OpenAlexW2074548288WikidataQ118592645 ScholiaQ118592645MaRDI QIDQ791258

Włodzimierz Greblicki, Mirosław Pawlak

Publication date: 1982

Published in: Information Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0020-0255(82)90036-6

zbMATH Keywords

rate of convergencemultiple Fourier seriesprobability of misclassificationBayes probability of errorlearning sequences of random lengthsweak and strong Bayes risk consistency

Mathematics Subject Classification ID

Classification and discrimination; cluster analysis (statistical aspects) (62H30) Nonparametric estimation (62G05)

Related Items

Classification via local multi-resolution projections, Wavelet-based estimation of generalized discriminant functions, Iterative Learning in Repetitive Optimal Control of Linear Dynamic Processes, A general approach to classification problems

Cites Work

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• Optimal convergence properties of variable knot, kernel, and orthogonal series methods for density estimation
• Properties of Hermite series estimation of probability density
• On convergence and growth of partial sums of Fourier series
• Convergence almost everywhere of certain singular integrals and multiple Fourier series
• Remarks on Some Nonparametric Estimates of a Density Function
• On the rate of convergence of nearest neighbor rules (Corresp.)
• Asymptotic efficiency of classifying procedures using the Hermite series estimate of multivariate probability densities (Corresp.)
• Classification Using the Fourier Series Estimate of Multivariate Density Functions
• Asymptotically optimal pattern recognition procedures with density estimates (Corresp.)
• Probability Inequalities for Sums of Bounded Random Variables
• A Nonparametric Estimate of a Multivariate Density Function
• Estimation of Probability Density by an Orthogonal Series
• The Estimation of Probability Densities and Cumulatives by Fourier Series Methods
• Asymptotically optimal discriminant functions for pattern classification
• On the convergence of multiple Fourier series
• Nonparametric Probability Density Estimation: I. A Summary of Available Methods