We prove the central limit theorem for the integrated square error of multivariate box-spline density estimators.

The aim of this paper is to apply the appropriate numerical, statistical and computer techniques to the construction of approximate solutions to nonlinear 2nd order stochastic differential equations modeling some engineering systems subject to large random external disturbances. This provides us with quantitative results on their asymptotic behavior.

The aim of this paper is to demonstrate how the appropriate numerical, statistical and computer techniques can be successfully applied to the construction of approximate solutions of stochastic differential equations modeling some engineering systems subject to large disturbances. In particular, the evolution in time of densities of stochastic processes solving such problems is discussed.

Se define un estimador no paramétrico, recursivo, de la función de regresión r(x) = E(Y/X = x), que se calcula a partir de un conjunto de n observaciones {(X1,Yi): i = 1, ..., n} del vector aleatorio (X,Y). Bajo la hipótesis de que los datos son idénticamente distribuidos pero no necesariamente independientes, lo que permite utilizar el estimador definido para estimar la función de autorregresión de una serie de tiempo, se obtienen resultados sobre la consistencia puntual débil (en probabilidad)...

The problem of nonparametric regression function estimation is considered using the complete orthonormal system of trigonometric functions or Legendre polynomials $e_k$, k=0,1,..., for the observation model $y_i=f\left(x_i\right)+{\eta }_i$, i=1,...,n, where the ${\eta }_i$ are independent random variables with zero mean value and finite variance, and the observation points $x_i\in [a,b]$, i=1,...,n, form a random sample from a distribution with density $\varrho \in L^1[a,b]$. Sufficient and necessary conditions are obtained for consistency in the sense of the errors $\parallel f-{\widehat{f}}_N\parallel ,|f\left(x\right){-}_N\left(x\right)|$, $x\in [a,b]$,...