An exact Rosenthal-type inequality for the third absolute moments is given, as well as a number of related results. Such results are useful in applications to Berry–Esseen bounds.

A well-known longstanding conjecture on the supremum of the tails of normalized sums of independent Rademacher random variables is disproved. A special case of this conjecture was recently disproved by A. Zhubr.

In this article, we consider the problem of criterion choice in information recovery and inference in a large-deviations (LD) context. Kitamura and Stutzer recognize that the Maximum Entropy Empirical Likelihood estimator can be given a LD justification (Kitamura and Stutzer, 2002). We...

Many well-known goodness-of-fit and symmetry tests are based on U- et V-statistics. Recent progress in the analysis of their large deviations enables to find new expressions for their local Bahadur efficiency in case of bounded kernels and to formulate the conditions of local optimality. For...

We consider the problem of testing whether the observations X1, ..., Xn of a time series are independent with unspecified (possibly nonidentical) distributions symmetric about a common known median. Various bounds on the distributions of serial correlation coefficients are proposed: exponential...

We propose an approach to measure the mobility immanent in regular Markov processes. For this purpose, we distinguish between mobility in equilibrium and mobility associated with convergence towards equilibrium. The former aspect is measured as the expectation of a functional, defined on the...

We propose here a review of the methods available to compute pattern statistics on text generated by a Markov source. Theoretical, but also numerical aspects are detailed for a wide range of techniques (exact, Gaussian, large deviations, binomial and compound Poisson). The SPatt package...

We use the theory of large deviations to investigate the large time behavior and the small noise asymptotics of random economic processes whose evolutions are governed by mean-reverting stochastic differential equations with (i) constant and (ii) state dependent noise terms. We explicitly show...