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In Martin et al (2003), we suggested an approach to general robustness studies in Bayesian Decision Theory and Inference, based on ε-contamination neighborhoods. In this note, we generalise the results considering neighborhoods based on norms, specifically, the supremum norm for utilities and the total variation norm for probability distributions. We provide tools to detect changes in preferences between alternatives under perturbations of the prior and/or the utility and the most sensitive direction....
The paper studies the estimation problem of individual weights of objects using a chemical balance weighing design under the restriction on the number times in which each object is weighed. Conditions under which the existence of an optimum chemical balance weighing design for objects implies the existence of an optimum chemical balance weighing design for objects are given. The existence of an optimum chemical balance weighing design for objects implies the existence of an optimum chemical...
"A high quantile is a quantile of order q with q close to one." A precise constructive definition of high quantiles is given and optimal estimates are presented.
This paper is a survey of recent results on some problems of supervised learning in the setting formulated by Cucker and Smale. Supervised learning, or learning-from-examples, refers to a process that builds on the base of available data of inputs and outputs , i = 1,...,m, a function that best represents the relation between the inputs x ∈ X and the corresponding outputs y ∈ Y. The goal is to find an estimator on the base of given data that approximates well the regression function of...
We present optimal upper bounds for expectations of order statistics from i.i.d. samples with a common distribution function belonging to the restricted family of probability measures that either precede or follow a given one in the star ordering. The bounds for families with monotone failure density and rate on the average are specified. The results are obtained by projecting functions onto convex cones of Hilbert spaces.
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