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Data-based decision rules about the convexity of the support of a distribution

Autor
Delicado, P.; Hernandez, A.; Lugosi, G.
Tipus d'activitat
Article en revista
Revista
Electronic journal of statistics
Data de publicació
2014-01-01
Volum
8
Número
1
Pàgina inicial
96
Pàgina final
129
DOI
https://doi.org/10.1214/14-EJS877 Obrir en finestra nova
Projecte finançador
Estadística y probabilidad orientada al análisis de datos discreto
URL
http://projecteuclid.org/euclid.ejs/1392041252 Obrir en finestra nova
Resum
Given n independent, identically distributed random vectors in R-d, drawn from a common density f, one wishes to find out whether the support of f is convex or not. In this paper we describe a decision rule which decides correctly for sufficiently largen, with probability 1, whenever f is bounded away from zero in its compact support. We also show that the assumption of boundedness is necessary. The rule is based on a statistic that is a second-orde U-statistic with a random kernel. Moreover, we...
Paraules clau
CLASSIFICATION, DENSITY LEVEL SETS, Discernibility between hypotheses, FRAMEWORK, ISOMAP, RATES, U-statistics, bootstrap subsampling, dimensionality reduction, set estimation
Grup de recerca
ADBD - Anàlisi de Dades Complexes per a les Decisions Empresarials

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