On the asymptotic properties of smoothed estimators of the classification error rate
type: Item
instance of: scholarly article
title: On the asymptotic properties of smoothed estimators of the classification error rate
zbMATH Open document ID: 0644.62069
DOI: 10.1016/0031-3203(88)90010-6
author: M. Pawlak
published in: Pattern Recognition
publication date: 1988-01-01T00:00:00Z
review text: A smoothed correction of the classification error rate counting estimate is examined. The consistency of the estimate under very general conditions is established. For normal distributions, asymptotic theory reveals that the relative deficiency of the counting estimate with respect to the smoothed one can tend to infinity as the sample size increases.
Mathematics Subject Classification ID: 62H30
zbMATH DE Number: 4050793
zbMATH Keywords: resubstitution method
zbMATH Keywords: Vapnik-Chervonenkis classes
zbMATH Keywords: efficiency
zbMATH Keywords: smoothed correction
zbMATH Keywords: classification error rate counting estimate
zbMATH Keywords: consistency
zbMATH Keywords: normal distributions
zbMATH Keywords: asymptotic theory
zbMATH Keywords: relative deficiency
Wikidata QID: Q118592631
MaRDI profile type: Publication
full work available at URL: 0031-3203(88)90010-6
OpenAlex ID: W1973909898
cites work: Q4097679
cites work: Enumeration of Seven-Argument Threshold Functions
cites work: On the Inequality of Cover and Hart in Nearest Neighbor Discrimination
cites work: Bounds for the uniform deviation of empirical measures
cites work: A distribution-free performance bound in error estimation (Corresp.)
cites work: Distribution-free performance bounds with the resubstitution error estimate (Corresp.)
cites work: Q3336497
cites work: Central limit theorems for empirical measures
cites work: Relative efficiency and deficiency of kernel type estimators of smooth distribution functions
cites work: Additive estimators for probabilities of correct classification
cites work: Sample-based classification procedures related to empiric distributions
cites work: Necessary and sufficient conditions for Bayes risk consistency of a recursive kernel classification rule (Corresp.)
cites work: Almost sure convergence of classification procedures using Hermite series density estimates
cites work: Deficiency
cites work: Probability Inequalities for Sums of Bounded Random Variables
cites work: Assessing the performance of an allocation rule
cites work: Relations between Weak and Uniform Convergence of Measures with Applications
cites work: Q3921991
cites work: Estimation of the probabilities of misclassification for a linear discriminant function in the univariate normal case
cites work: Common Structure of Smoothing Techniques in Statistics
cites work: Bibliography on estimation of misclassification
cites work: Smoothed additive estimators for non-error rates in multiple discriminant analysis
cites work: On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
cites work: Estimation of dependences based on empirical data. Transl. from the Russian by Samuel Kotz
cites work: Nonparametric estimates of probability densities
cites work: Some special Vapnik-Chervonenkis classes
description: scientific article; zbMATH DE number 4050793