Distance estimation to the exponential class with applications to cluster stars

J. Cárcamo Urtiaga, A. Baíllo Moreno, K. Getman

We propose a new methodology to measure deviations from the class of exponential random variables based on the estimation of various integral probability metrics.
Specifically, we consider the problem of estimating the Wasserstein and Zolotarev metrics, as well as the normalized versions of these distances, between a positive random variable and an exponential variable with the same mean.
We obtain sharp asymptotic results related to the plug-in estimators of these metrics and compare them with the finite-sample distributions via simulations. The practical use of our proposal is illustrated analysing a massive data set from X-ray astronomy consisting in the photon interarrival times of stellar objects (mainly stars) in the Orion Nebula region obtained as a result of the Chandra Orion Ultradeep Project.

Palabras clave: Wasserstein distance; Zolotarev metric; plug-in estimator; asymptotic distribution; integrated Brownian bridge; integrated empirical process; probability metrics.

X03.2 Fiabilidad
7 de septiembre de 2016  10:00
0.09 - Aula de proyectos 2

C. J. Pérez González, A. Fernández Rodríguez

J. E. Ruiz Castro