Empirical estimator of the regularity index of a probability measure
Kybernetika (2012)
- Volume: 48, Issue: 4, page 589-599
- ISSN: 0023-5954
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topBerlinet, Alain, and Servien, Rémi. "Empirical estimator of the regularity index of a probability measure." Kybernetika 48.4 (2012): 589-599. <http://eudml.org/doc/246522>.
@article{Berlinet2012,
abstract = {The index of regularity of a measure was introduced by Beirlant, Berlinet and Biau [1] to solve practical problems in nearest neighbour density estimation such as removing bias or selecting the number of neighbours. These authors proved the weak consistency of an estimator based on the nearest neighbour density estimator. In this paper, we study an empirical version of the regularity index and give sufficient conditions for its weak and strong convergence without assuming absolute continuity or other global properties of the underlying measure.},
author = {Berlinet, Alain, Servien, Rémi},
journal = {Kybernetika},
keywords = {regularity index; Lebesgue point; small ball probability; regularity index; Lebesgue point; small ball probability},
language = {eng},
number = {4},
pages = {589-599},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Empirical estimator of the regularity index of a probability measure},
url = {http://eudml.org/doc/246522},
volume = {48},
year = {2012},
}
TY - JOUR
AU - Berlinet, Alain
AU - Servien, Rémi
TI - Empirical estimator of the regularity index of a probability measure
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 4
SP - 589
EP - 599
AB - The index of regularity of a measure was introduced by Beirlant, Berlinet and Biau [1] to solve practical problems in nearest neighbour density estimation such as removing bias or selecting the number of neighbours. These authors proved the weak consistency of an estimator based on the nearest neighbour density estimator. In this paper, we study an empirical version of the regularity index and give sufficient conditions for its weak and strong convergence without assuming absolute continuity or other global properties of the underlying measure.
LA - eng
KW - regularity index; Lebesgue point; small ball probability; regularity index; Lebesgue point; small ball probability
UR - http://eudml.org/doc/246522
ER -
References
top- J. Beirlant, A. Berlinet, G. Biau, 10.1007/s10463-007-0112-x, Ann. Inst. Statist. Math. 60 (2008), 651-677. Zbl1169.62024MR2434416DOI10.1007/s10463-007-0112-x
- A. Berlinet, S. Levallois, Higher order analysis at Lebesgue points., In: G. G. Roussas Festschrift - Asymptotics in Statistics and Probability (M. L. Puri, ed.), 2000, pp. 17-32.
- A. Berlinet, R. Servien, 10.1080/10485252.2011.567334, J. Nonparametr. Statist. 23 (2011), 633-643. MR2836281DOI10.1080/10485252.2011.567334
- L. Devroye, G. Lugosi, Combinatorial Methods in Density Estimation., Springer, New York 2001. Zbl0964.62025MR1843146
- R. M. Dudley, Real Analysis and Probability., Chapman and Hall, New York 1989. Zbl1023.60001MR0982264
- W. Rudin, Real and Complex Analysis., McGraw-Hill, New York 1987. Zbl1038.00002MR0924157
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