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Effet des erreurs de mesure sur l'évaluation de l'efficacité d'un traitement

Christian Heuchenne (1993)

Mathématiques et Sciences Humaines

L’effet d’un traitement T sur une compétence Y peut être exprimé par le coefficient de régression partiel β Y T avec contrôle de la compétence initiale X . Quand Y et X sont mesurées avec erreurs par y et x → , cet effet se manifeste par le coefficient β y T dans la régression de y sur T et x → . Le biais entre β Y T et β y T est explicité, discuté et montré systématique si X et T sont corrélés. L’importance de bien spécifier le modèle, dont une condition nécessaire et suffisante d’identification est donnée, est mise en...

Efficient robust estimation of time-series regression models

Pavel Čížek (2008)

Applications of Mathematics

The paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However, contrary to the existing methods, the first-order asymptotic behavior...

Eliminating transformations for nuisance parameters in linear regression models with type I constraints

Pavla Kunderová (2007)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The linear regression model in which the vector of the first order parameter is divided into two parts: to the vector of the useful parameters and to the vector of the nuisance parameters is considered. The type I constraints are given on the useful parameters. We examine eliminating transformations which eliminate the nuisance parameters without loss of information on the useful parameters.

Estimación de registros desconocidos en series de datos.

Miguel Sánchez García, Luis Javier López Martín (1985)

Trabajos de Estadística e Investigación Operativa

Se dispone de dos o más series de datos, de las cuales al menos una no se conoce completamente. Se supone que las series se pueden modelizar con la hipótesis lineal; así como que existe alguna estructura de correlación entre ellas. Se desarrollan dos modelos para estimar los valores desconocidos de la(s) serie(s) de datos.

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 ∈ 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 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 .

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