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Multivariate models with constraints confidence regions

Lubomír Kubáček (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In multivariate linear statistical models with normally distributed observation matrix a structure of a covariance matrix plays an important role when confidence regions must be determined. In the paper it is assumed that the covariance matrix is a linear combination of known symmetric and positive semidefinite matrices and unknown parameters (variance components) which are unbiasedly estimable. Then insensitivity regions are found for them which enables us to decide whether plug-in approach can...

Note on a Calibration Problem: Selected Results and Extensions of Professor Kubáček’s

Gejza Wimmer, Viktor Witkovský (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Professor Lubomír Kubáček has provided exceptional contributions to mathematical statistics and its applications. Because of his excellent knowledge in mathematical statistics as well as in the different fields of natural and especially technical sciences, he contributed to solution of a large number of real world problems. The continuation of Professor Kubáček’s scientific work and his scientific school is demonstrated by the results of his numerous students. Here we present just one illustration...

On the Equivalence between Orthogonal Regression and Linear Model with Type-II Constraints

Sandra Donevska, Eva Fišerová, Karel Hron (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Orthogonal regression, also known as the total least squares method, regression with errors-in variables or as a calibration problem, analyzes linear relationship between variables. Comparing to the standard regression, both dependent and explanatory variables account for measurement errors. Through this paper we shortly discuss the orthogonal least squares, the least squares and the maximum likelihood methods for estimation of the orthogonal regression line. We also show that all mentioned approaches...

Outliers in models with constraints

Lubomír Kubáček (2006)

Kybernetika

Outliers in univariate and multivariate regression models with constraints are under consideration. The covariance matrix is assumed either to be known or to be known only partially.

Quantiles conditionnels

Sandrine Poiraud-Casanova, Christine Thomas-Agnan (1998)

Journal de la société française de statistique

Sensitivity analysis in singular mixed linear models with constraints

Eva Fišerová, Lubomír Kubáček (2003)

Kybernetika

The singular mixed linear model with constraints is investigated with respect to an influence of inaccurate variance components on a decrease of the confidence level. The algorithm for a determination of the boundary of the insensitivity region is given. It is a set of all shifts of variance components values which make the tolerated decrease of the confidence level only. The problem about geometrical characterization of the confidence domain is also presented.

Stacked regression with restrictions

Tomasz Górecki (2005)

Discussiones Mathematicae Probability and Statistics

When we apply stacked regression to classification we need only discriminant indices which can be negative. In many situations, we want these indices to be positive, e.g., if we want to use them to count posterior probabilities, when we want to use stacked regression to combining classification. In such situation, we have to use leastsquares regression under the constraint βₖ ≥ 0, k = 1,2,...,K. In their earlier work [5], LeBlanc and Tibshirani used an algorithm given in [4]. However, in this paper...

Suitability of linearization of nonlinear problems not only in biology and medicine

Jana Vrbková (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Biology and medicine are not the only fields that present problems unsolvable through a linear models approach. One way to overcome this obstacle is to use nonlinear methods, even though these are not as thoroughly explored. Another possibility is to linearize and transform the originally nonlinear task to make it accessible to linear methods. In this aricle I investigate an easy and quick criterion to verify suitability of linearization of nonlinear problems via Taylor series expansion so that...

Tests lineales para contrastes con hipótesis oblicuas.

Cristina Rueda Sabater (1991)

Trabajos de Estadística

En contrastes de hipótesis oblicuas para medias normales se ha demostrado la dominación del test de razón de verosimilitud (TRV). En este contexto consideramos estadísticos definidos por combinaciones lineales de las medias muestrales obteniendo tests para coeficientes fijos y aleatorios. En ambos casos los tests óptimos no tienen en cuenta toda la información del modelo original siendo adecuados para situaciones con hipótesis menos restrictivas. En la obtención de tests con coeficientes aleatorios...

Uncertainty of coordinates and looking for dispersion of GPS receiver

Pavel Tuček, Jaroslav Marek (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The aim of the paper is to show some possible statistical solution of the estimation of the dispersion of the GPS receiver. The presented method (based on theory of linear model with additional constraints of type I) can serve for an improvement of the accuracy of estimators of coordinates acquired from the GPS receiver.

Weakly nonlinear regression model with constraints I: nonlinear hypothesis

Lubomír Kubácek, Eva Tesaríková (2005)

Discussiones Mathematicae Probability and Statistics

The problem considered is under which conditions in weakly nonlinear regression model with constraints I a weakly nonlinear hypothesis can be tested by linear methods. The aim of the paper is to find a region around the approximate value of the regression parameter with the following property. If we are certain that the actual value of the regression parameter is in this region, then the linear method of testing can be used without any significant deterioration of the inference.

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