Number of found documents: 1656
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Implicitly weighted robust estimation of quantiles in linear regression
Kalina, Jan; Vidnerová, Petra
2019 - English
Estimation of quantiles represents a very important task in econometric regression modeling, while the standard regression quantiles machinery is well developed as well as popular with a large number of econometric applications. Although regression quantiles are commonly known as robust tools, they are vulnerable to the presence of leverage points in the data. We propose here a novel approach for the linear regression based on a specific version of the least weighted squares estimator, together with an additional estimator based only on observations between two different novel quantiles. The new methods are conceptually simple and comprehensible. Without the ambition to derive theoretical properties of the novel methods, numerical computations reveal them to perform comparably to standard regression quantiles, if the data are not contaminated by outliers. Moreover, the new methods seem much more robust on a simulated dataset with severe leverage points. Keywords: regression quantiles; robust regression; outliers; leverage points Fulltext is available at external website.
Implicitly weighted robust estimation of quantiles in linear regression

Estimation of quantiles represents a very important task in econometric regression modeling, while the standard regression quantiles machinery is well developed as well as popular with a large number ...

Kalina, Jan; Vidnerová, Petra
Ústav informatiky, 2019

A Robustified Metalearning Procedure for Regression Estimators
Kalina, Jan; Neoral, A.
2019 - English
Metalearning represents a useful methodology for selecting and recommending a suitable algorithm or method for a new dataset exploiting a database of training datasets. While metalearning is potentially beneficial for the analysis of economic data, we must be aware of its instability and sensitivity to outlying measurements (outliers) as well as measurement errors. The aim of this paper is to robustify the metalearning process. First, we prepare some useful theoretical tools exploiting the idea of implicit weighting, inspired by the least weighted squares estimator. These include a robust coefficient of determination, a robust version of mean square error, and a simple rule for outlier detection in linear regression. We perform a metalearning study for recommending the best linear regression estimator for a new dataset (not included in the training database). The prediction of the optimal estimator is learned over a set of 20 real datasets with economic motivation, while the least squares are compared with several (highly) robust estimators. We investigate the effect of variable selection on the metalearning results. If the training as well as validation data are considered after a proper robust variable selection, the metalearning performance is improved remarkably, especially if a robust prediction error is used. Keywords: model choice; computational statistics; robustness; variable selection Available in digital repository of the ASCR
A Robustified Metalearning Procedure for Regression Estimators

Metalearning represents a useful methodology for selecting and recommending a suitable algorithm or method for a new dataset exploiting a database of training datasets. While metalearning is ...

Kalina, Jan; Neoral, A.
Ústav informatiky, 2019

MAT TRIAD 2019: Book of Abstracts
Bok, J.; Hartman, David; Hladík, M.; Rozložník, Miroslav
2019 - English
This volume contains the Book of abstracts of the 8th International Conference on Matrix Analysis and its Applications, MAT TRIAD 2019. The MATTRIAD conferences represent a platform for researchers in a variety of aspects of matrix analysis and its interdisciplinary applications to meet and share interests and ideas. The conference topics include matrix and operator theory and computation, spectral problems, applications of linear algebra in statistics, statistical models, matrices and graphs as well as combinatorial matrix theory and others. The goal of this event is to encourage further growth of matrix analysis research including its possible extension to other fields and domains. Keywords: proceedings; conference; matrix analysis Available on request at various institutes of the ASCR
MAT TRIAD 2019: Book of Abstracts

This volume contains the Book of abstracts of the 8th International Conference on Matrix Analysis and its Applications, MAT TRIAD 2019. The MATTRIAD conferences represent a platform for researchers ...

Bok, J.; Hartman, David; Hladík, M.; Rozložník, Miroslav
Ústav informatiky, 2019

Rozhodování za neurčitosti: Pohled matematika na plánované hospodářství
Rohn, Jiří
2019 - Czech
V práci jsou popsány hlavní výsledky neoficiálního ekonomicko-matematického výzkumu provedeného v letech 1973-1980 pracovníky Ekonomicko-matematické laboratoře Ekonomického ústavu ČSAV a MFF (J. Bouška, J. Rohn a B. Kalendovský). Keywords: Leontěvův model; intervalová data; zaručené řešení; neexistence; matice 28 x 28 Available in digital repository of the ASCR
Rozhodování za neurčitosti: Pohled matematika na plánované hospodářství

V práci jsou popsány hlavní výsledky neoficiálního ekonomicko-matematického výzkumu provedeného v letech 1973-1980 pracovníky Ekonomicko-matematické laboratoře Ekonomického ústavu ČSAV a MFF (J. ...

Rohn, Jiří
Ústav informatiky, 2019

Absolute Value Mapping
Rohn, Jiří
2019 - English
We prove a necessary and sufficient condition for an absolute value mapping to be bijective. This result simultaneously gives a characterization of unique solvability of an absolute value equation for each right-hand side. Keywords: absolute value mapping; bijectivity; interval matrix; regularity; absolute value equation; unique solvability Available in a digital repository NRGL
Absolute Value Mapping

We prove a necessary and sufficient condition for an absolute value mapping to be bijective. This result simultaneously gives a characterization of unique solvability of an absolute value equation for ...

Rohn, Jiří
Ústav informatiky, 2019

A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix
Lukšan, Ladislav; Vlček, Jan
2019 - English
In this contribution, we propose a new hybrid method for minimization of nonlinear least squares. This method is based on quasi-Newton updates, applied to an approximation A of the Jacobian matrix J, such that AT f = JT f. This property allows us to solve a linear least squares problem, minimizing ∥Ad+f∥ instead of solving the normal equation ATAd+JT f = 0, where d ∈ Rn is the required direction vector. Computational experiments confirm the efficiency of the new method. Keywords: nonlinear least squares; hybrid methods; trust-region methods; quasi-Newton methods; numerical algorithms; numerical experiments Available at various institutes of the ASCR
A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix

In this contribution, we propose a new hybrid method for minimization of nonlinear least squares. This method is based on quasi-Newton updates, applied to an approximation A of the Jacobian matrix J, ...

Lukšan, Ladislav; Vlček, Jan
Ústav informatiky, 2019

On the Optimal Initial Conditions for an Inverse Problem of Model Parameter Estimation - a Complementarity Principle
Matonoha, Ctirad; Papáček, Š.
2019 - English
This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatio-temporal measurements of fluorescent particle concentration, see [6, 1, 3, 4, 5]. More precisely, we continue to look for an optimal bleaching pattern used in FRAP (Fluorescence Recovery After Photobleaching), being the initial condition of the Fickian diffusion equation maximizing a sensitivity measure. As follows, we define an optimization problem and we show the special feature (so-called complementarity principle) of the optimal binary-valued initial conditions. Keywords: parameter identification; bleaching pattern; initial boundary value problem; sensitivity measure Available in digital repository of the ASCR
On the Optimal Initial Conditions for an Inverse Problem of Model Parameter Estimation - a Complementarity Principle

This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatio-temporal measurements of ...

Matonoha, Ctirad; Papáček, Š.
Ústav informatiky, 2019

Jak jsme (z)řídili ústav aneb Od Centrálního výpočetního střediska ČSAV k Ústavu informatiky AV ČR
Šebesta, Václav
2019 - Czech
Jak jsme (z)řídili ústav aneb Od Centrálního výpočetního střediska ČSAV k Ústavu informatiky AV ČR Available in a digital repository NRGL
Jak jsme (z)řídili ústav aneb Od Centrálního výpočetního střediska ČSAV k Ústavu informatiky AV ČR

Jak jsme (z)řídili ústav aneb Od Centrálního výpočetního střediska ČSAV k Ústavu informatiky AV ČR

Šebesta, Václav
Ústav informatiky, 2019

Overdetermined Absolute Value Equations
Rohn, Jiří
2019 - English
We consider existence, uniqueness and computation of a solution of an absolute value equation in the overdetermined case. Keywords: absolute value equations; overdetermined system Available in a digital repository NRGL
Overdetermined Absolute Value Equations

We consider existence, uniqueness and computation of a solution of an absolute value equation in the overdetermined case.

Rohn, Jiří
Ústav informatiky, 2019

Generalization of a Theorem on Eigenvalues of Symmetric Matrices
Rohn, Jiří
2019 - English
We prove that the product of a symmetric positive semide nite matrix and a symmetric matrix has all eigenvalues real. Keywords: symmetric matrix; positive semide nite matrix; real spectrum Available in a digital repository NRGL
Generalization of a Theorem on Eigenvalues of Symmetric Matrices

We prove that the product of a symmetric positive semide nite matrix and a symmetric matrix has all eigenvalues real.

Rohn, Jiří
Ústav informatiky, 2019

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