Simulation in conjugate distributions with application to the estimation of the Cramer transform in R-d

Let X: X-1,X-2.... be a sequence of i. i.d. [R-d-valued random variables wi th distribution F. An algorithm for the simulation of random vectors with d istribution dF(t) (x) e(t,x) dF (x)/phi(t), where phi (t) := Ee((t,X)) (cf. [2]) is used for the estimation of the Cramer transformation H (x) := sup, ((t: X) - log phi (t)). This method which belongs to the class of "accepta nce-rejection" techniques, is fast and uses a random sieve on the sequence (X-i) (i greater than or equal to 1); it does not assume any prior knowledg e on F or phi. We state the asymptotic properties of this estimator calcula ted on a n-sample of simulated r.v. 's with distribution F,. We also presen t some numerical simulations. (C) Academie des Sciences/Elsevier, Paris.