An efficient estimator for the expectation $\int fP̣$ is constructed, where $P$ is a Gibbs random field, and $f$ is a local statistic, i. e. a functional depending on a finite number of coordinates. The estimator coincides with the empirical estimator under the conditions stated in Greenwood and Wefelmeyer [6], and covers the known special cases, namely the von Mises statistic for the i.i.d. underlying fields and the case of one-dimensional Markov chains.

Let ${𝕖}_t={(e_{t1},\cdots ,e_{tp})}^{\text{'}}$ be a $p$-dimensional nonnegative strict white noise with finite second moments. Let $h_{ij}\left(x\right)$ be nondecreasing functions from $[0,\infty )$ onto $[0,\infty )$ such that $h_{ij}\left(x\right)\le x$ for $i,j=1,\cdots ,p$. Let $𝕌=\left(u_{ij}\right)$ be a $p\times p$ matrix with nonnegative elements having all its roots inside the unit circle. Define a process ${𝕏}_t={(X_{t1},\cdots ,X_{tp})}^{\text{'}}$ by $$X_{tj}=u_{j1}{h}_{1j}\left(X_{t-1,1}\right)+\cdots +u_{jp}{h}_{pj}\left(X_{t-1,p}\right)+e_{tj}$$ for $j=1,\cdots ,p$. A method for estimating $𝕌$ from a realization ${𝕏}_1,\cdots ,{𝕏}_n$ is proposed. It is proved that the estimators are strongly consistent.

The most general sequence, with Gumbel margins, generated by maxima procedures in an auto-regressive way (one step) is defined constructively and its properties obtained; some remarks for statistical estimation are presented.

Let $𝐗$ and $𝐘$ be stationarily cross-correlated multivariate stationary sequences. Assume that all values of $𝐘$ and all but one values of $𝐗$ are known. We determine the best linear interpolation of the unknown value on the basis of the known values and derive a formula for the interpolation error matrix. Our assertions generalize a result of Budinský [1].

Implicit sampling is a sampling scheme for particle filters, designed to move particles one-by-one so that they remain in high-probability domains. We present a new derivation of implicit sampling, as well as a new iteration method for solving the resulting algebraic equations.

Implicit sampling is a sampling scheme for particle filters, designed to move particles one-by-one so that they remain in high-probability domains. We present a new derivation of implicit sampling, as well as a new iteration method for solving the resulting algebraic equations.

En este trabajo se introduce el modelo ARE(I) con indicador de nivel mínimo J.l, parámetro que generaliza el modelo ARO) con errores exponenciales y se analiza desde un punto de vista bayesiano, obteniéndose una familia de distribuciones conjugadas para el hiperparámetro que describe el modelo.

El presente artículo recoge los resultados de una investigación llevada a cabo con el fin de analizar, desde la perspectiva de la no similaridad, las distribuciones de los distintos estadísticos planteados por Dickey y Fuller para contrastar la presencia de raíz unitaria. Asimismo, se definen zonas de rechazo y aceptación de las hipótesis nulas para cada estadístico, considerando las distintas distribuciones del mismo, y se estudian las situaciones con las que nos podemos encontrar de cara a deducir...