We generalize the results for statistical functionals given by [Fernholz, 1983] and [Serfling, 1980] to M estimates for samples drawn for an ergodic and stationary martingale sequence. In a first step, we take advantage of some recent results on the uniform convergency of the empirical...

In this article consistency and asymptotic normality of the quasi-maximum likelihood esti- mator (QMLE) in the class of polynomial augmented generalized autoregressive conditional heteroscedasticity models (GARCH) is proven. The result extend the results of (Berkes et al., 2003) and (Francq and...

In this article, consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) in the class of polynomial augmented generalized autoregressive conditional heteroscedasticity models (GARCH) is proven. The result extends the results of the standard GARCH model to the class...

Idempotence is a well-known property of functionals of location. It means that the value of the functional at a singular distribution must be identically to the mass point of this distribution. First, we explain the role of idempotence in the known axiomizations of location functionals. Then we...

A new kind of entropy will be introduced generalizing both the differential entropy and the cumulative (residual) entropy. The generalization is twofold. Firstly, we define the entropy for cumulative distribution functions (cdf) and survivor functions (sf) simultaneously instead of densities,...