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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...

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.

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...

Some results envolving the concepts of moment generating function and affinity between distribution functions. Extension for r k-dimensional normal distribution functions.

Antonio Dorival Campos (1999)

Qüestiió

We present a function ρ (F1, F2, t) which contains Matusita's affinity and expresses the affinity between moment generating functions. An interesting results is expressed through decomposition of this affinity ρ (F1, F2, t) when the functions considered are k-dimensional normal distributions. The same decomposition remains true for other families of distribution functions. Generalizations of these results are also presented.

Statistical aspects of associativity for copulas

José M. González-Barrios (2010)

Kybernetika

In this paper we study in detail the associativity property of the discrete copulas. We observe the connection between discrete copulas and the empirical copulas, and then we propose a statistic that indicates when an empirical copula is associative and obtain its main statistical properties under independence. We also obtained asymptotic results of the proposed statistic. Finally, we study the associativity statistic under different copulas and we include some final remarks about associativity...

Symmetries of random discrete copulas

Arturo Erdely, José M. González–Barrios, Roger B. Nelsen (2008)

Kybernetika

In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry of copulas.

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