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...

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...

A problem of goodness-of-fit test for ergodic diffusion processes is presented. In the null hypothesis the drift of the diffusion is supposed to be in a parametric form with unknown shift parameter. Two Cramer–von Mises type test statistics are studied. The first test uses the local time...

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>

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...

Dzhaparidze and Spreij (Stoch Process Appl, 54:165–174, <CitationRef CitationID="CR5">1994</CitationRef>) showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of continuous stochastic processes. This class contains...</citationref>

Based on observations <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$X_1,\dots ,X_n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo stretchy="false">…</mo> <mo>,</mo> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </mrow> </math> </EquationSource> </InlineEquation> of successive generations of a discrete-parameter Galton–Watson branching process, one wishes to predict whether extinction or explosion will ultimately occur. This problem can be formulated as a simple...</equationsource></equationsource></inlineequation>