Let p1 ≤ p2 and consider estimating a fixed set {x : p1 ≤ f(x) ≤ p2} by the random set {x : p1 ≤ f̂n(x) ≤ p2}, where f̂n is a consistent estimator of the continuous function f . This paper gives consistency conditions for these sets, and provides a new method to construct confidence regions from empirical averages of sets. The method can also be used to construct confidence regions for sets of th...

Access controls ensure that all direct accesses to objects are authorized by means of user identification. However, in some scenarios it is also necessary to continuously check the identity of the user in order to avoid malicious behaviors such as person exchanges immediately after the initial authentication phase. Aim of this work is to propose a methodology based on a balanced mix of strong a...

The distribution of an inhomogeneous Wiener process is determined by the mean function m(t) ss EW(t) and the variance function b(t) = V^(W(t)) which depend on unknown parameter d _ 0 . Observations are assumed to be in discrete time points where the sample size tends to infinity. Using the general theory of Ibragimow, Hasminskij [2] sufficient conditions for consistency of MLE i?n are establish...