Displaying similar documents to “Reliability of modules with load-sharing components.”

Cyclic random motions in ℝ d -space with directions

Aimé Lachal (2006)

ESAIM: Probability and Statistics

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We study the probability distribution of the location of a particle performing a cyclic random motion in ℝ d . The particle can take possible directions with different velocities and the changes of direction occur at random times. The speed-vectors as well as the support of the distribution form a polyhedron (the first one having constant sides and the other expanding with time ). The distribution of the location of the particle is made up of two components: a singular component (corresponding...

Probabilities of discrepancy between minima of cross-validation, Vapnik bounds and true risks

Przemysław Klęsk (2010)

International Journal of Applied Mathematics and Computer Science

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Two known approaches to complexity selection are taken under consideration: n-fold cross-validation and structural risk minimization. Obviously, in either approach, a discrepancy between the indicated optimal complexity (indicated as the minimum of a generalization error estimate or a bound) and the genuine minimum of unknown true risks is possible. In the paper, this problem is posed in a novel quantitative way. We state and prove theorems demonstrating how one can calculate pessimistic...

Random thresholds for linear model selection

Marc Lavielle, Carenne Ludeña (2008)

ESAIM: Probability and Statistics

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A method is introduced to select the significant or non null mean terms among a collection of independent random variables. As an application we consider the problem of recovering the significant coefficients in non ordered model selection. The method is based on a convenient random centering of the partial sums of the ordered observations. Based on -statistics methods we show consistency of the proposed estimator. An extension to unknown parametric distributions is considered. ...