We consider the estimation of error distributions in least squares identiication of distributed parameter systems. Asymptotic properties of approximate error sequences are developed. In particular, we examine consistency and asymptotic normality of empirical estimates of the error distribution. The consistency obtained is analogous to the Glivenko-Cantelli theorem. For asymptotic normality, we ...

It is well known that classical propositional logic can be interpreted in intuitionistic propositional logic. In particular Glivenko’s theorem states that a formula is provable in the former iff its double negation is provable in the latter. We extend Glivenko’s theorem and show that for every involutive substructural logic there exists a minimum substructural logic that contains the first via ...

In this note we will study upper bounds of random variables of the type sup A∈A |ν n (A) − ν(A)| , where A is a class of sets that needs to fulll certain assumptions. These bounds are important tools in the analysis of learning processes and probabilistic theories of pattern recognition. The presentation given here is based on [DGL96].

Statistical Learning Theory comprises a collection of techniques that have been developed in order to theoretically analyse the performance of neural network and other “learning” algorithms. In this paper, a number of recent results in statistical learning theory are summarised in the context of nonlinear system identification. A top-down approach to the problem is taken, leading to the stateme...