Least squares estimation of Generalized Space Time AutoRegressive (GSTAR) model and its properties

In this paper we studied a least squares estimation parameters of the Generalized Space Time AutoRegressive (GSTAR) model and its properties, especially in consistency and asymptotic normality. We use R software to estimate the GSTAR parameter and apply the model toward real phenomena of data, such as an oil production data at volcanic layer.

Reconstructie van de aardkorst met tomografie (Reconstruction of the earth’s crust by tomography)

Röntgenfoto’s, echo’s en reconstructies van de aardkorst zijn drie toepassingen waarbij tomografie een grote rol speelt. Tomografie is een methode om eigenschappen van een onbereikbaar gebied te bepalen met behulp van stralen of drukgolven. De aardkorst bestaat uit allerlei verschillende steenlagen. Als op grote diepte een aardbeving plaatsvindt...

Estimating a concave distribution function from data corrupted with additive noise

We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on (0, ?). For the maximum likelihood (ML) estimator and least squares (LS) estimator, we state qualitative properties, prove consistency and propose a computational...

Estimation of a convex function: Characterizations and asymptotic theory

We study nonparametric estimation of convexregression and density functions by methods of least squares (in the regression and density cases) and maximum likelihood (in the density estimation case).We provide characterizations of these estimators, prove that they are consistent and establish their asymptotic distributions at a fixed point of...

A canonical process for estimation of convex functions: The "invelope" of integrated Brownian motion +t4

A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively. We call this process “the invelope” and show that it is an almost surely uniquely defined function of integrated Brownian...