Empirical estimator of the regularity index of a probability measure

Title:

Empirical estimator of the regularity index of a probability measure

Creator:

Berlinet, Aalin and Servien, Rémy

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:67b2952c-00bc-4986-977f-0629432254ef
uuid:67b2952c-00bc-4986-977f-0629432254ef

Subject:

regularity index, Lebesgue point, and small ball probability

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The index of regularity of a measure was introduced by Beirlant, Berlinet and Biau \cite{bbb} 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[589]-599

Source:

Kybernetika | 2012 Volume:48 | Number:4

Harvested from:

CDK

Metadata only:

false