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We consider here a multivariate sample Xj = (X1.j > ... > Xi.j), 1 ≤ j ≤ n, where the Xj, 1 ≤ j ≤ n, are independent i-dimensional extremal vectors with suitable unknown location and scale parameters λ and δ respectively. Being interested in linear estimation of these parameters, we consider the multivariate sample Zj, 1 ≤ j ≤ n, of the order statistic of largest values and their concomitants, and the best linear unbiased estimators of λ and δ based on such multivariate sample. Computational...
A robust version of the Ordinary Least Squares accommodating the idea of weighting the order statistics of the squared residuals (rather than directly the squares of residuals) is recalled and its properties are studied. The existence of solution of the corresponding extremal problem and the consistency under heteroscedasticity is proved.
In this paper we comment on some papers written by Jerzy K. Baksalary. In particular, we draw attention to the development process of some specific research ideas and papers now that some time, more than 15 years, has gone after their publication.
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.
En el presente trabajo se realiza un estudio de la envoltura convexa de una muestra normal bivariante, analizando la distribución de la pendiente de sus aristas. En base a ello se propone un estimador del coeficiente de correlación de la población, investigando algunas propiedades del mismo.
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 -optimum estimators. The aim of the paper is to contribute to a numerical solution...
The paper deals with an optimal estimation of the quadratic function , where is a known matrix, in the model . The distribution of 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 .
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.
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