Infill statistics, that is, statistical inference based on very dense observations over a fixed domain has become of late a subject of growing importance. On the other hand, it is a known phenomenon that in many cases infill statistics do not provide optimal rates. The degree of sub-optimality...

<Para ID="Par1">We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure convergence of our estimators, together with a quadratic strong...</para>

<Para ID="Par1">In this paper we investigate the large-sample behaviour of the maximum likelihood estimate (MLE) of the unknown parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\theta $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">θ</mi> </math> </EquationSource> </InlineEquation> for processes following the model <Equation ID="Equ38"> <EquationSource Format="TEX">$$\begin{aligned} d\xi _{t}=\theta f(t)\xi _{t}\,dt+d\mathrm {B}_t, \end{aligned}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink" display="block"> <mrow> <mtable columnspacing="0.5ex"> <mtr> <mtd columnalign="right"> <mrow> <mi>d</mi> <msub> <mi mathvariant="italic">ξ</mi> <mi>t</mi> </msub> <mo>=</mo> <mi mathvariant="italic">θ</mi> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <msub> <mi mathvariant="italic">ξ</mi>...</msub></mrow></mtd></mtr></mtable></mrow></math></equationsource></equationsource></equation></equationsource></equationsource></inlineequation></para>

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...

We study a least square-type estimator for an unknown parameter in the drift coefficient of a stochastic differential equation with additive fractional noise of Hurst parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$H1/2$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>H</mi> <mo></mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </math> </EquationSource> </InlineEquation>. The estimator is based on discrete time observations of the stochastic differential...</equationsource></equationsource></inlineequation>

Denote the integer lattice points in the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$N$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>N</mi> </math> </EquationSource> </InlineEquation>-dimensional Euclidean space by <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\mathbb {Z}^N$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> <mi>N</mi> </msup> </math> </EquationSource> </InlineEquation> and assume that <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$X_\mathbf{n}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>X</mi> <mi mathvariant="bold">n</mi> </msub> </math> </EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\mathbf{n} \in \mathbb {Z}^N$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="bold">n</mi> <mo>∈</mo> <msup> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> <mi>N</mi> </msup> </mrow> </math> </EquationSource> </InlineEquation> is a linear random field. Sharp rates of convergence of histogram estimates...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

In this paper we investigate the problem of detecting a change in the drift parameters of a generalized Ornstein–Uhlenbeck process which is defined as the solution of <Equation ID="Equ23"> <EquationSource Format="TEX">$$\begin{aligned} dX_t=(L(t)-\alpha X_t) dt + \sigma dB_t \end{aligned}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink" display="block"> <mrow> <mtable columnspacing="0.5ex"> <mtr> <mtd columnalign="right"> <mrow> <mi>d</mi> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>=</mo> <mrow> <mo stretchy="false">(</mo> <mi>L</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>-</mo> <mi mathvariant="italic">α</mi> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo stretchy="false">)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>+</mo> <mi mathvariant="italic">σ</mi>...</mrow></mtd></mtr></mtable></mrow></math></equationsource></equationsource></equation>