Large deviations for estimators of unknown probabilities, with applications in risk theory

Claudio Macci (1)

1 Dipartimento di Matematica

We present large deviation results for estimators of unknown probabilities which satisfy a suitable exponential decay condition. These results provide some extensions of the large deviation estimates in Macci and Petrella (2006). Furthermore we propose a classical approach which is different from the one presented in Ganesh et al. (1998) and we cannot say that the Bayesian approach is more conservative as in that paper.

Mots clés: Large deviations; Varadhan's Lemma; Level crossing probability; Compound Poisson process; Brownian motion

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Claudio Macci. Large deviations for estimators of unknown probabilities, with applications in risk theory. Statistics and Probability Letters, 2010, 81 (1), pp.16. ⟨10.1016/j.spl.2010.09.013⟩. ⟨hal-00698869⟩