We consider adaptive Bayesian estimation of both drift and diffusion coefficient parameters for ergodic multidimensional diffusion processes based on sampled data. Under a general condition on the discretization step of the sampled data, three kinds of adaptive Bayes type estimators are proposed...

Identifying a model by the penalized contrast procedure, we give an analytical estimation of misfitting subsets in the specific case of a least squares contrast. Then, specifying the statistical model, this allows to determine penalization rates ensuring a consistent identification. Applications...

We consider the model selection problem for ergodic diffusion processes based on sampled data. The adaptive estimators for parameters of drift and diffusion coefficients are used in order to construct Akaike’s information criterion (AIC) type model selection statistics. Asymptotic properties...

One-dimensional indexed bilinear (BL) models are widely used for modeling non Gaussian time series. Extending BL models to multidimensional indexed (spatial) SBL one, yields a novel class of models which are capable of taking into account the important characteristic of non Gaussianity and...

We consider the problem of the construction of the asymptotically distribution free test by the observations of ergodic diffusion process. It is supposed that under the basic hypothesis the trend coefficient depends on a finite-dimensional parameter and we study the Cramér-von Mises type...

The objective of the paper is to identify and investigate all possible types of asymptotic behavior for the maximum likelihood estimators of the unknown parameters in the second-order linear stochastic ordinary differential equation driven by Gaussian white noise. The emphasis is on the...

We prove the asymptotic normality of kernel estimators of second- and higher-order product densities (and of the pair correlation function) for spatially homogeneous (and isotropic) point processes observed on a sampling window <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$W_n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>W</mi> <mi>n</mi> </msub> </math> </EquationSource> </InlineEquation>, which is assumed to expand unboundedly in all...</equationsource></equationsource></inlineequation>

We study the problem of parameter estimation for stochastic differential equations with small noise and fast oscillating parameters. Depending on how fast the intensity of the noise goes to zero relative to the homogenization parameter, we consider three different regimes. For each regime, we...

This paper has to do with a Cramér-von Mises test for symmetry of the error distribution in a class of absolutely regular and non-necessarily stationary heteroscedastic models. The test statistic is based on the empirical characteristic function. Its convergence, as well as that of the...

Dans ce papier, nous nous intéressons à l’estimation de la fonction de régression par une approche non-paramétrique par noyau. Nous établissons la normalité asymptotique, pour une famille générale d’estimateurs récursifs à noyau de la fonction de régression, sous une hypothèse de...