1. Empirical estimator of the regularity index of a probability measure
- Creator:
- Berlinet, Aalin and Servien, Rémy
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- regularity index, Lebesgue point, and small ball probability
- Language:
- English
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public