Displaying 21 – 40 of 62

Showing per page

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 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 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 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.

Estimation of polynomials in the regression model

Júlia Volaufová (1982)

Aplikace matematiky

Let 𝐘 be an n -dimensional random vector which is N n ( 𝐀 0 , 𝐊 ) distributed. A minimum variance unbiased estimator is given for f ( o ) provided f is an unbiasedly estimable functional of an unknown k -dimensional parameter 0 .

Estimation of the first order parameters in the twoepoch linear model

Karel Hron (2007)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The linear regression model, where the mean value parameters are divided into stable and nonstable part in each of both epochs of measurement, is considered in this paper. Then, equivalent formulas of the best linear unbiased estimators of this parameters in both epochs using partitioned matrix inverse are derived.

Estimation of the hazard function in a semiparametric model with covariate measurement error

Marie-Laure Martin-Magniette, Marie-Luce Taupin (2009)

ESAIM: Probability and Statistics

We consider a failure hazard function, conditional on a time-independent covariate Z, given by η γ 0 ( t ) f β 0 ( Z ) . The baseline hazard function η γ 0 and the relative risk f β 0 both belong to parametric families with θ 0 = ( β 0 , γ 0 ) m + p . The covariate Z has an unknown density and is measured with an error through an additive error model U = Z + ε where ε is a random variable, independent from Z, with known density f ε . We observe a n-sample (Xi, Di, Ui), i = 1, ..., n, where Xi is the minimum between the failure time and the censoring time, and...

Currently displaying 21 – 40 of 62