We consider a chaotic system with a double-scroll attractor proposed by Elwakil, composing with a second-order system, which has low-dimensional multiple invariant subspaces and multi-level on-off intermittency. This type of composite system always includes a skew-product structure and some invariant subspaces, which are associated with different levels of laminar phase. In order for the level of laminar phase be adjustable, we adopt a nonlinear function with saturation characteristic to tune the...

Planteamos el modelo lineal sobre variables dummy difusas asociadas a variables cuantitativas codificadas o cualitativas. En el modelo bicriterio aparecen las mismas dificultades conceptuales que se presentan en el caso multicriterio, pero su desarrollo resulta mucho más ágil y transparente. Resolvemos las ecuaciones normales, caracterizando el conjunto de soluciones y encontramos finalmente las funciones paramétricas estimables para este modelo.

Continuando el desarrollo del modelo lineal sobre dos variables dummy difusas, encontramos expresiones para las descomposiciones clásicas en sumas de cuadrados y estudiamos sus distribuciones bajo hipótesis de normalidad. Damos una interpretación geométrica del ajuste cuando las variables numéricas explicativas se ven sometidas a una codificación difusa de tipo semilineal y contrastamos en estos casos la mejora de este nuevo modelo respecto de la regresión sobre las variables originales. Concluimos...

By using three theorems (Oktaba and Kieloch [3]) and Theorem 2.2 (Srivastava and Khatri [4]) three results are given in formulas (2.1), (2.8) and (2.11). They present asymptotically normal confidence intervals for the determinant $|{\sigma }^2\sum |$ in the MGM model $(U,XB,{\sigma }^2\sum \otimes V)$, $\sum >0$, scalar ${\sigma }^2>0$, with a matrix $V\ge 0$. A known $n\times p$ random matrix $U$ has the expected value $E\left(U\right)=XB$, where the $n\times d$ matrix $X$ is a known matrix of an experimental design, $B$ is an unknown $d\times p$ matrix of parameters and ${\sigma }^2\sum \otimes V$ is the covariance matrix of $U,\otimes$ being the symbol of the Kronecker...

Linear relations, containing measurement errors in input and output data, are taken into account in this paper. Parameters of these so-called errors-in-variables (EIV) models can be estimated by minimizing the total least squares (TLS) of the input-output disturbances. Such an estimate is highly non-linear. Moreover in some realistic situations, the errors cannot be considered as independent by nature. Weakly dependent ($\alpha$- and $\varphi$-mixing) disturbances, which are not necessarily stationary nor identically...

In the paper necessary and sufficient conditions for the existence and an explicit expression for the Bayes invariant quadratic unbiased estimate of the linear function of the variance components are presented for the mixed linear model $𝐭=𝐗\beta +ϵ$, $𝐄\left(𝐭\right)=𝐗\beta$, $\mathrm{𝐕𝐚𝐫}\left(𝐭\right)={\mathbf{0}}_{\mathbf{1}}{𝐔}_{\mathbf{1}}+{\mathbf{0}}_{\mathbf{2}}{𝐔}_{\mathbf{2}}+{\mathbf{0}}_{\mathbf{3}}{𝐔}_{\mathbf{3}}$, with three unknown variance components in the normal case. An application to some examples from the analysis of variance is given.

In the paper an explicit expression for the Bayes invariant quadratic unbiased estimate of the linear function of the variance components is presented for the mixed linear model $𝐭=𝐗\beta +ϵ$, $𝐄\left(𝐭\right)=𝐗\beta$, $𝐃\left(𝐭\right)={\mathbf{0}}_{\mathbf{1}}{𝐔}_{\mathbf{1}}+{\mathbf{0}}_{\mathbf{2}}{𝐔}_{\mathbf{2}}$ with the unknown variance componets in the normal case. The matrices ${𝐔}_{\mathbf{1}}$, ${𝐔}_{\mathbf{2}}$ may be singular. Applications to two examples of the analysis of variance are given.

The paper deals with the asymptotic distribution of the least squares estimator of a change point in a regression model where the regression function has two phases --- the first linear and the second quadratic. In the case when the linear coefficient after change is non-zero the limit distribution of the change point estimator is normal whereas it is non-normal if the linear coefficient is zero.

The following three results for the general multivariate Gauss-Markoff model with a singular covariance matrix are given or indicated. $1^{\circ }$ determinant ratios as products of independent chi-square distributions, $2^{\circ }$ moments for the determinants and $3^{\circ }$ the method of obtaining approximate densities of the determinants.

Dans deux articles, dont voici le premier, sont présentés deux exemples d'analyse statistique par des méthodes factorielles. Le cadre mathématique de l'exposé est algébrique. La présente formulation de ces problèmes s'appuie sur l'expérience d'enseignement menée à l'UER de Mathématiques, Logique Formelle et Informatique de l'Université René-Descartes, ainsi que sur une rédaction parue dans les actes du Colloque «Analyse des données en architecture et urbanisme» [5].

Although many words have been written about two recent directional (regression) quantile concepts, their applications, and the algorithms for computing associated (regression) quantile regions, their software implementation is still not widely available, which, of course, severely hinders the dissemination of both methods. Wanting to partly fill in the gap here, we provide all the codes needed for computing and plotting the multivariate (regression) quantile regions in Octave and MATLAB, describe...

Recently, the eminently popular standard quantile regression has been generalized to the multiple-output regression setup by means of directional regression quantiles in two rather interrelated ways. Unfortunately, they lead to complicated optimization problems involving parametric programming, and this may be the main obstacle standing in the way of their wide dissemination. The presented R package modQR is intended to address this issue. It originates as a quite faithful translation of the authors'...