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On univariate and bivariate aging for dependent lifetimes with Archimedean survival copulas

Franco Pellerey (2008)

Kybernetika

Let 𝐗 = ( X , Y ) be a pair of exchangeable lifetimes whose dependence structure is described by an Archimedean survival copula, and let 𝐗 t = [ ( X - t , Y - t ) | X > t , Y > t ] denotes the corresponding pair of residual lifetimes after time t , with t ≥ 0 . This note deals with stochastic comparisons between 𝐗 and 𝐗 t : we provide sufficient conditions for their comparison in usual stochastic and lower orthant orders. Some of the results and examples presented here are quite unexpected, since they show that there is not a direct correspondence between univariate...

One singular multivariate linear model with nuisance parameters

Pavla Kunderová (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The multivariate linear model, in which the matrix of the first order parameters is divided into two matrices: to the matrix of the useful parameters and to the matrix of the nuisance parameters, is considered.

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....

Optimal solutions of multivariate coupling problems

Ludger Rüschendorf (1995)

Applicationes Mathematicae

Some necessary and some sufficient conditions are established for the explicit construction and characterization of optimal solutions of multivariate transportation (coupling) problems. The proofs are based on ideas from duality theory and nonconvex optimization theory. Applications are given to multivariate optimal coupling problems w.r.t. minimal l p -type metrics, where fairly explicit and complete characterizations of optimal transportation plans (couplings) are obtained. The results are of interest...

Optimization of the size of nonsensitiveness regions

Eva Lešanská (2002)

Applications of Mathematics

The problem is to determine the optimum size of nonsensitiveness regions for the level of statistical tests. This is closely connected with the problem of the distribution of quadratic forms.

Orbital semilinear copulas

Tarad Jwaid, Bernard de Baets, Hans de Meyer (2009)

Kybernetika

We introduce four families of semilinear copulas (i.e. copulas that are linear in at least one coordinate of any point of the unit square) of which the diagonal and opposite diagonal sections are given functions. For each of these families, we provide necessary and sufficient conditions under which given diagonal and opposite diagonal functions can be the diagonal and opposite diagonal sections of a semilinear copula belonging to that family. We focus particular attention on the family of orbital...

Outliers in models with constraints

Lubomír Kubáček (2006)

Kybernetika

Outliers in univariate and multivariate regression models with constraints are under consideration. The covariance matrix is assumed either to be known or to be known only partially.

Overview of Recent Results in Growth-curve-type Multivariate Linear Models

Ivan Žežula, Daniel Klein (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The Extended Growth Curve Model (ECGM) is a multivariate linear model connecting different multivariate regression models in sample subgroups through common variance matrix. It has the form: Y = ∑ i = 1 k X i B i Z i ' + e , vec ( e ) ∼ N n × p 0 , Σ ⊗ I n . Here, matrices X i contain subgroup division indicators, and Z i corresponding regressors. If k = 1 , we speak about (ordinary) Growth Curve Model. The model has already its age (it dates back to 1964), but it has many important applications. That is why it is still intensively studied. Many articles investigating...

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