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Asymptotics of Monte Carlo maximum likelihood estimators

Miasojedow B., Niemiro W., Palczewski J., Rejchel W.

Probability and Mathematical Statistics

2016

Vol. 36, Fasc. 2

295--310

We describe Monte Carlo approximation to the maximum likelihood estimator in models with intractable norming constants and explanatory variables. We consider both sources of randomness (due to the initial sample and to Monte Carlo simulations) and prove asymptotical normality of the estimator.

An Empirical Functional Central Limit Theorem for weakly dependent sequences

Prieur C.

Probability and Mathematical Statistics

2002

Vol. 22, Fasc. 2

259--287

In this paper we obtain a Functional Central Limit Theorem for the empirical process of a stationary sequence under a new weak dependence condition introduced by Doukhan and Louhichi [5]. This result improves on the Empirical Functional Central Limit Theorem in Doukhan and Louhichi [5]. Our proof relies on new moment inequalities and on a Central Limit Theorem. Techniques of proofs come from Louhichi [12] and Rio [16], respectively. We also deduce a rate of convergence in a Marcinkiewicz-Zygmund Strong Law.

Locations of extreme values of the empirical process

Randjiou Y.

Probability and Mathematical Statistics

2001

Vol. 21, Fasc. 1

57--70

Let αn be a uniform empirical process and μn (respectively, νn the unique location of its maximum (respectively, minimum). We establish a “liminf” iterated logarithm law for |μn – νn|