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On a class of estimators in a multivariate RCA(1) model

Zuzana Prášková, Pavel Vaněček (2011)

Kybernetika

This work deals with a multivariate random coefficient autoregressive model (RCA) of the first order. A class of modified least-squares estimators of the parameters of the model, originally proposed by Schick for univariate first-order RCA models, is studied under more general conditions. Asymptotic behavior of such estimators is explored, and a lower bound for the asymptotic variance matrix of the estimator of the mean of random coefficient is established. Finite sample properties are demonstrated...

On a distance between estimable functions.

Concepción Arenas Solá (1989)

Qüestiió

In this paper we study the main properties of a distance introduced by C.M. Cuadras (1974). This distance is a generalization of the well-known Mahalanobis distance between populations to a distance between parametric estimable functions inside the multivariate analysis of variance model. Reduction of dimension properties, invariant properties under linear automorphisms, estimation of the distance, distribution under normality as well as the interpretation as a geodesic distance are studied and...

On a general structure of the bivariate FGM type distributions

Sayed Mohsen Mirhosseini, Mohammad Amini, Ali Dolati (2015)

Applications of Mathematics

In this paper, we study a general structure for the so-called Farlie-Gumbel-Morgenstern (FGM) family of bivariate distributions. Through examples we show how to use the proposed structure to study dependence properties of the FGM type distributions by a general approach.

On a problem by Schweizer and Sklar

Fabrizio Durante (2012)

Kybernetika

We give a representation of the class of all n -dimensional copulas such that, for a fixed m ∈ ℕ , 2 ≤ m < n , all their m -dimensional margins are equal to the independence copula. Such an investigation originated from an open problem posed by Schweizer and Sklar.

On an asymmetric extension of multivariate Archimedean copulas based on quadratic form

Elena Di Bernardino, Didier Rullière (2016)

Dependence Modeling

An important topic in Quantitative Risk Management concerns the modeling of dependence among risk sources and in this regard Archimedean copulas appear to be very useful. However, they exhibit symmetry, which is not always consistent with patterns observed in real world data. We investigate extensions of the Archimedean copula family that make it possible to deal with asymmetry. Our extension is based on the observation that when applied to the copula the inverse function of the generator of an...

On Bartlett's test for correlation between time series

Jiří Anděl, Jaromír Antoch (1998)

Kybernetika

An explicit formula for the correlation coefficient in a two-dimensional AR(1) process is derived. Approximate critical values for the correlation coefficient between two one-dimensional AR(1) processes are tabulated. They are based on Bartlett’s approximation and on an asymptotic distribution derived by McGregor. The results are compared with critical values obtained from a simulation study.

On best affine unbiased covariance-preserving prediction of factor scores.

Heinz Neudecker (2004)

SORT

This paper gives a generalization of results presented by ten Berge, Krijnen,Wansbeek & Shapiro. They examined procedures and results as proposed by Anderson & Rubin, McDonald, Green and Krijnen, Wansbeek & ten Berge.We shall consider the same matter, under weaker rank assumptions. We allow some moments, namely the variance Ω of the observable scores vector and that of the unique factors, Ψ, to be singular. We require T' Ψ T &gt; 0, where T Λ T' is a Schur decomposition of Ω. As...

On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators

Elena Di Bernardino, Didier Rullière (2013)

Dependence Modeling

We study the impact of certain transformations within the class of Archimedean copulas. We give some admissibility conditions for these transformations, and define some equivalence classes for both transformations and generators of Archimedean copulas. We extend the r-fold composition of the diagonal section of a copula, from r ∈ N to r ∈ R. This extension, coupled with results on equivalence classes, gives us new expressions of transformations and generators. Estimators deriving directly from these...

On computations with causal compositional models

Vladislav Bína, Radim Jiroušek (2015)

Kybernetika

The knowledge of causal relations provides a possibility to perform predictions and helps to decide about the most reasonable actions aiming at the desired objectives. Although the causal reasoning appears to be natural for the human thinking, most of the traditional statistical methods fail to address this issue. One of the well-known methodologies correctly representing the relations of cause and effect is Pearl's causality approach. The paper brings an alternative, purely algebraic methodology...

On conditional independence and log-convexity

František Matúš (2012)

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

If conditional independence constraints define a family of positive distributions that is log-convex then this family turns out to be a Markov model over an undirected graph. This is proved for the distributions on products of finite sets and for the regular Gaussian ones. As a consequence, the assertion known as Brook factorization theorem, Hammersley–Clifford theorem or Gibbs–Markov equivalence is obtained.

On Conditional Value at Risk (CoVaR) for tail-dependent copulas

Piotr Jaworski (2017)

Dependence Modeling

The paper deals with Conditional Value at Risk (CoVaR) for copulas with nontrivial tail dependence. We show that both in the standard and the modified settings, the tail dependence function determines the limiting properties of CoVaR as the conditioning event becomes more extreme. The results are illustrated with examples using the extreme value, conic and truncation invariant families of bivariate tail-dependent copulas.

On copulas that generalize semilinear copulas

Juan Fernández Sánchez, Manuel Úbeda-Flores (2012)

Kybernetika

We study a wide class of copulas which generalizes well-known families of copulas, such as the semilinear copulas. We also study corresponding results for the case of quasi-copulas.

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