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Optimal chemical balance weighing designs for v + 1 objects

Bronisław Ceranka, Małgorzata Graczyk (2003)

Kybernetika

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 p = v objects implies the existence of an optimum chemical balance weighing design for p = v + 1 objects are given. The existence of an optimum chemical balance weighing design for p = v + 1 objects implies the existence of an optimum chemical...

Optimal estimators in learning theory

V. N. Temlyakov (2006)

Banach Center Publications

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 x i and outputs y i , 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 f z on the base of given data z : = ( ( x ₁ , y ₁ ) , . . . , ( x m , y m ) ) that approximates well the regression function f ρ of...

Optimal mean-variance bounds on order statistics from families determined by star ordering

Tomasz Rychlik (2002)

Applicationes Mathematicae

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.

Optimal model selection in density estimation

Matthieu Lerasle (2012)

Annales de l'I.H.P. Probabilités et statistiques

In order to calibrate a penalization procedure for model selection, the statistician has to choose a shape for the penalty and a leading constant. In this paper, we study, for the marginal density estimation problem, the resampling penalties as general estimators of the shape of an ideal penalty. We prove that the selected estimator satisfies sharp oracle inequalities without remainder terms under a few assumptions on the marginal density s and the collection of models. We also study the slope heuristic,...

Optimal nonlinear transformations of random variables

Aldo Goia, Ernesto Salinelli (2010)

Annales de l'I.H.P. Probabilités et statistiques

In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh–Ritz method, is introduced. Asymptotic properties of the estimator are proved, providing an upper bound for the rate of convergence under suitable mild conditions....

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