Displaying similar documents to “The multiple regression model where independent variables are measured unprecisely.”

On estimation of parameters in the bivariate linear errors-in-variables model

Anna Czapkiewicz (1999)

Applicationes Mathematicae

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We discuss some methods of estimation in bivariate errors-in-variables linear models. We also suggest a method of constructing consistent estimators in the case when the error disturbances have the normal distribution with unknown parameters. It is based on the theory of estimating variance components in linear models. A simulation study is presented which compares this estimator with the maximum likelihood one.

On some alternative forms equivalent to Kruskal's condition for OLSE to be BLUE.

Gabriela Beganu (2007)

RACSAM

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The necessary and sufficient condition for the ordinary least squares estimators (OLSE) to be the best linear unbiased estimators (BLUE) of the expected mean in the general univariate linear regression model was given by Kruskal (1968) using a coordinate-free approach. The purpose of this article is to present in the same manner some alternative forms of this condition and to prove two of the Haberman’s equivalent conditions in a different and simpler way. The results obtained in the...

On a class of estimators in a multivariate RCA(1) model

Zuzana Prášková, Pavel Vaněček (2011)

Kybernetika

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This work deals with a multivariate random coefficient autoregressive model (RCA) of the first order. A class of modified least-squares estimators of the parameters of the model, originally proposed by Schick for univariate first-order RCA models, is studied under more general conditions. Asymptotic behavior of such estimators is explored, and a lower bound for the asymptotic variance matrix of the estimator of the mean of random coefficient is established. Finite sample properties are...

Spatial prediction of the mark of a location-dependent marked point process: How the use of a parametric model may improve prediction

Tomáš Mrkvička, François Goreaud, Joël Chadoeuf (2011)

Kybernetika

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We discuss the prediction of a spatial variable of a multivariate mark composed of both dependent and explanatory variables. The marks are location-dependent and they are attached to a point process. We assume that the marks are assigned independently, conditionally on an unknown underlying parametric field. We compare (i) the classical non-parametric Nadaraya-Watson kernel estimator based on the dependent variable (ii) estimators obtained under an assumption of local parametric model...

Estimation of nuisance parameters for inference based on least absolute deviations

Wojciech Niemiro (1995)

Applicationes Mathematicae

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Statistical inference procedures based on least absolute deviations involve estimates of a matrix which plays the role of a multivariate nuisance parameter. To estimate this matrix, we use kernel smoothing. We show consistency and obtain bounds on the rate of convergence.

Theory of parameter estimation

Ryszard Zieliński (1997)

Banach Center Publications

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0. Introduction and summary. The analysis of data from the gravitational-wave detectors that are currently under construction in several countries will be a challenging problem. The reason is that gravitational-vawe signals are expected to be extremely weak and often very rare. Therefore it will be of great importance to implement optimal statistical methods to extract all possible information about the signals from the noisy data sets. Careful statistical analysis based on correct application...

On the equality of the ordinary least squares estimators and the best linear unbiased estimators in multivariate growth-curve models.

Gabriela Beganu (2007)

RACSAM

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It is well known that there were proved several necessary and sufficient conditions for the ordinary least squares estimators (OLSE) to be the best linear unbiased estimators (BLUE) of the fixed effects in general linear models. The purpose of this article is to verify one of these conditions given by Zyskind [39, 40]: there exists a matrix Q such that ΩX = XQ, where X and Ω are the design matrix and the covariance matrix, respectively. It will be shown the accessibility of this condition...