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Scatter halfspace depth: Geometric insights

Stanislav Nagy (2020)

Applications of Mathematics

Scatter halfspace depth is a statistical tool that allows one to quantify the fitness of a candidate covariance matrix with respect to the scatter structure of a probability distribution. The depth enables simultaneous robust estimation of location and scatter, and nonparametric inference on these. A handful of remarks on the definition and the properties of the scatter halfspace depth are provided. It is argued that the currently used notion of this depth is well suited especially for symmetric...

Scenario generation with distribution functions and correlations

Michal Kaut, Arnt-Gunnar Lium (2014)

Kybernetika

In this paper, we present a method for generating scenarios for two-stage stochastic programs, using multivariate distributions specified by their marginal distributions and the correlation matrix. The margins are described by their cumulative distribution functions and we allow each margin to be of different type. We demonstrate the method on a model from stochastic service network design and show that it improves the stability of the scenario-generation process, compared to both sampling and a...

Seemingly unrelated regression models

Lubomír Kubáček (2013)

Applications of Mathematics

The cross-covariance matrix of observation vectors in two linear statistical models need not be zero matrix. In such a case the problem is to find explicit expressions for the best linear unbiased estimators of both model parameters and estimators of variance components in the simplest structure of the covariance matrix. Univariate and multivariate forms of linear models are dealt with.

Selective F tests for sub-normal models

Célia Maria Pinto Nunes, João Tiago Mexia (2003)

Discussiones Mathematicae Probability and Statistics

F tests that are specially powerful for selected alternatives are built for sub-normal models. In these models the observation vector is the sum of a vector that stands for what is measured with a normal error vector, both vectors being independent. The results now presented generalize the treatment given by Dias (1994) for normal fixed-effects models, and consider the testing of hypothesis on the ordering of mean values and components.

Self-adaptation of parameters in a learning classifier system ensemble machine

Maciej Troć, Olgierd Unold (2010)

International Journal of Applied Mathematics and Computer Science

Self-adaptation is a key feature of evolutionary algorithms (EAs). Although EAs have been used successfully to solve a wide variety of problems, the performance of this technique depends heavily on the selection of the EA parameters. Moreover, the process of setting such parameters is considered a time-consuming task. Several research works have tried to deal with this problem; however, the construction of algorithms letting the parameters adapt themselves to the problem is a critical and open problem...

Semiparametric estimation of the parameters of multivariate copulas

Eckhard Liebscher (2009)

Kybernetika

In the paper we investigate properties of maximum pseudo-likelihood estimators for the copula density and minimum distance estimators for the copula. We derive statements on the consistency and the asymptotic normality of the estimators for the parameters.

Sharp equivalence between ρ- and τ-mixing coefficients

Rémi Peyre (2013)

Studia Mathematica

For two σ-algebras 𝓐 and ℬ, the ρ-mixing coefficient ρ(𝓐,ℬ) between 𝓐 and ℬ is the supremum correlation between two real random variables X and Y which are 𝓐 - resp. ℬ-measurable; the τ'(𝓐,ℬ) coefficient is defined similarly, but restricting to the case where X and Y are indicator functions. It has been known for a long time that the bound ρ ≤ Cτ'(1 + en | log τ'|) holds for some constant C; in this article, we show that C = 1 works and is best possible.

Shluková analysa

Adolf Filáček, Václav Koutník, Jiří Vondráček (1977)

Časopis pro pěstování matematiky

Shuffles of Min.

Piotr Mikusinski, Howard Sherwood, Michael D. Taylor (1992)

Stochastica

Copulas are functions which join the margins to produce a joint distribution function. A special class of copulas called shuffles of Min is shown to be dense in the collection of all copulas. Each shuffle of Min is interpreted probabilistically. Using the above-mentioned results, it is proved that the joint distribution of any two continuously distributed random variables X and Y can be approximated uniformly, arbitrarily closely by the joint distribution of another pair X* and Y* each of which...

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