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Estimation for misspecified ergodic diffusion processes from discrete observations

Masayuki Uchida, Nakahiro Yoshida (2011)

ESAIM: Probability and Statistics

The joint estimation of both drift and diffusion coefficient parameters is treated under the situation where the data are discretely observed from an ergodic diffusion process and where the statistical model may or may not include the true diffusion process. We consider the minimum contrast estimator, which is equivalent to the maximum likelihood type estimator, obtained from the contrast function based on a locally Gaussian approximation of the transition density. The asymptotic normality of the...

Estimation for misspecified ergodic diffusion processes from discrete observations

Masayuki Uchida, Nakahiro Yoshida (2012)

ESAIM: Probability and Statistics

The joint estimation of both drift and diffusion coefficient parameters is treated under the situation where the data are discretely observed from an ergodic diffusion process and where the statistical model may or may not include the true diffusion process. We consider the minimum contrast estimator, which is equivalent to the maximum likelihood type estimator, obtained from the contrast function based on a locally Gaussian approximation of the transition density. The asymptotic normality of...

Estimation functions and uniformly most powerful tests for inverse Gaussian distribution

Ion Vladimirescu, Radu Tunaru (2003)

Commentationes Mathematicae Universitatis Carolinae

The aim of this article is to develop estimation functions by confidence regions for the inverse Gaussian distribution with two parameters and to construct tests for hypotheses testing concerning the parameter λ when the mean parameter μ is known. The tests constructed are uniformly most powerful tests and for testing the point null hypothesis it is also unbiased.

Estimation in autoregressive model with measurement error

Jérôme Dedecker, Adeline Samson, Marie-Luce Taupin (2014)

ESAIM: Probability and Statistics

Consider an autoregressive model with measurement error: we observe Zi = Xi + εi, where the unobserved Xi is a stationary solution of the autoregressive equation Xi = gθ0(Xi − 1) + ξi. The regression function gθ0 is known up to a finite dimensional parameter θ0 to be estimated. The distributions of ξ1 and X0 are unknown and gθ belongs to a large class of parametric regression functions. The distribution of ε0is completely known. We propose an estimation procedure with a new criterion computed as...

Estimation in connecting measurements with constraints of type II

Jaroslav Marek (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper is a continuation of the paper [6]. It dealt with parameter estimation in connecting two–stage measurements with constraints of type I. Unlike the paper [6], the current paper is concerned with a model with additional constraints of type II binding parameters of both stages. The article is devoted primarily to the computational aspects of algorithms published in [5] and its aim is to show the power of 𝐇 * -optimum estimators. The aim of the paper is to contribute to a numerical solution...

Estimation in models driven by fractional brownian motion

Corinne Berzin, José R. León (2008)

Annales de l'I.H.P. Probabilités et statistiques

Let {bH(t), t∈ℝ} be the fractional brownian motion with parameter 0<H<1. When 1/2<H, we consider diffusion equations of the type X(t)=c+∫0tσ(X(u)) dbH(u)+∫0tμ(X(u)) du. In different particular models where σ(x)=σ or σ(x)=σ  x and μ(x)=μ or μ(x)=μ  x, we propose a central limit theorem for estimators of H and of σ based on regression methods. Then we give tests of the hypothesis on σ for these models. We also consider functional estimation on σ(⋅)...

Estimation in universal models with restrictions

Eva Fišerová (2004)

Discussiones Mathematicae Probability and Statistics

In modelling a measurement experiment some singularities can occur even if the experiment is quite standard and simple. Such an experiment is described in the paper as a motivation example. It is presented in the papar how to solve these situations under special restrictions on model parameters. The estimability of model parameters is studied and unbiased estimators are given in explicit forms.

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