Giorgio Celant

Bayes Factors and Maximum Entropy Distribution with Application to Bayesian Tests

In this paper we propose the analysis and the solution of some parametric two-sided tests, combining the Bayes factors logic with the maximum entropy method, that allows to obtain the less informative a priori probability distribution, taking into account the amount of initial information available to the experimenter.

A Convergence Result for a Class of Asymptotically Linear Estimators

This article provides the distribution of the last exit for strongly consistent estimators. Namely, we consider a small neighborhood of the (almost sure) limit and state the asymptotic distribution of the last time the estimator is outside this neighborhood. Such problems have been considered in the literature by various authors; this article extends these results in a semi-parametric frame. An application to adaptive estimation is provided.

Upper bounds for the error in some interpolation and extrapolation designs

This article deals with probabilistic upper bounds for the error in functional estimation defined on some interpolation and extrapolation designs, when the function to estimate is supposed to be analytic. The error pertaining to the estimate may depend on various factors: the frequency of observations on the knots, the position and number of the knots, and also on the error committed when approximating the function through its Taylor expansion. When the number of observations is fixed, then all these parameters are determined by the choice of the design and by the choice estimator of the unknown function. The scope of the article is therefore to determine a rule for the minimal number of observation required to achieve an upper bound of the error on the estimate with a given maximal probability.

Exact Solutions to the Problem of Predicting a vast Class of Weakly Stationary, Linearly Singular, Discrete-Parameter Stochastic Processes

It is well-known that a weakly stationary discrete-parameter stochastic process, X t with t ∈ Z (set of integers), is the sum. of two components: one is regular (R t ) and the other is singular (S t ) (Wald’s theorem). In statistical literature, the following hypothesis is given: S t = 0, ∀ t. This hypothesis is arbitrary because it is easy to show the existence of singular processes and furthermore we do not have at our disposal a statistical test in order to state, looking at the data, if X t = R t or X t = R t + S t or X t = S t . In order to prove that a singular process exists, we need to construct it.