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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 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.

Estimation of a quadratic function of the parameter of the mean in a linear model

Júlia Volaufová, Peter Volauf (1989)

Aplikace matematiky

The paper deals with an optimal estimation of the quadratic function β ' 𝐃 β , where β ∈ ℛ k , 𝐃 is a known k × k matrix, in the model 𝐘 , 𝐗 β , σ 2 𝐈 . The distribution of 𝐘 is assumed to be symmetric and to have a finite fourth moment. An explicit form of the best unbiased estimator is given for a special case of the matrix 𝐗 .

Estimation of dispersion in nonlinear regression models with constraints

Lubomír Kubáček, Eva Tesaříková (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Dispersion of measurement results is an important parameter that enables us not only to characterize not only accuracy of measurement but enables us also to construct confidence regions and to test statistical hypotheses. In nonlinear regression model the estimator of dispersion is influenced by a curvature of the manifold of the mean value of the observation vector. The aim of the paper is to find the way how to determine a tolerable level of this curvature.

Estimation of parameters in a network reliability model with spatial dependence

Ian Hepburn Dinwoodie (2010)

ESAIM: Probability and Statistics

An iterative method based on a fixed-point property is proposed for finding maximum likelihood estimators for parameters in a model of network reliability with spatial dependence. The method is shown to converge at a geometric rate under natural conditions on data.

Estimation of parameters in a network reliability model with spatial dependence

Ian Hepburn Dinwoodie (2005)

ESAIM: Probability and Statistics

An iterative method based on a fixed-point property is proposed for finding maximum likelihood estimators for parameters in a model of network reliability with spatial dependence. The method is shown to converge at a geometric rate under natural conditions on data.

Estimation of parameters of mean and variance in two-stage linear models

Júlia Volaufová (1987)

Aplikace matematiky

The paper deals with the estimation of unknown vector parameter of mean and scalar parameters of variance as well in two-stage linear model, which is a special type of mixed linear model. The necessary and sufficient condition for the existence of uniformly best unbiased estimator of parameter of means is given. The explicite formulas for these estimators and for the estimators of the parameters of variance as well are derived.

Currently displaying 41 – 60 of 106