Functional approach for excess mass estimation in the density model

Details Functional approach for excess mass estimation in the density model Functional approach for excess mass estimation in the density model

2007-11-06

arxiv.org/abs/0711.0807v1

Electronic Journal of Statistics 2007, Vol. 1, 449-472

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-EJS079 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

10.1214/07-EJS079

We consider a multivariate density model where we estimate the excess mass of the unknown probability density $f$ at a given level $\nu>0$ from $n$ i.i.d. observed random variables. This problem has several applications such as multimodality testing, density contour clustering, anomaly detection, classification and so on. For the first time in the literature we estimate the excess mass as an integrated functional of the unknown density $f$. We suggest an estimator and evaluate its rate of convergence, when $f$ belongs to general Besov smoothness classes, for several risk measures. A particular care is devoted to implementation and numerical study of the studied procedure. It appears that our procedure improves the plug-in estimator of the excess mass.

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