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Implicitly weighted robust estimation of quantiles in linear regression
Kalina, Jan; Vidnerová, Petra
2019 - anglický
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.
Klíčová slova:
regression quantiles; robust regression; outliers; leverage points
Dokument je dostupný na externích webových stránkách.
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 ...
A Robustified Metalearning Procedure for Regression Estimators
Kalina, Jan; Neoral, A.
2019 - anglický
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.
Klíčová slova:
model choice; computational statistics; robustness; variable selection
Plné texty jsou dostupné v digitálním repozitáři Akademie Věd.
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 ...
MAT TRIAD 2019: Book of Abstracts
Bok, J.; Hartman, David; Hladík, M.; Rozložník, Miroslav
2019 - anglický
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.
Klíčová slova:
proceedings; conference; matrix analysis
Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd.
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 ...
Rozhodování za neurčitosti: Pohled matematika na plánované hospodářství
Rohn, Jiří
2019 - český
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).
Klíčová slova:
Leontěvův model; intervalová data; zaručené řešení; neexistence; matice 28 x 28
Plné texty jsou dostupné v digitálním repozitáři Akademie Věd.
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. ...
Absolute Value Mapping
Rohn, Jiří
2019 - anglický
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.
Klíčová slova:
absolute value mapping; bijectivity; interval matrix; regularity; absolute value equation; unique solvability
Plné texty jsou dostupné v digitálním repozitáři NUŠL
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 ...
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 - anglický
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.
Klíčová slova:
nonlinear least squares; hybrid methods; trust-region methods; quasi-Newton methods; numerical algorithms; numerical experiments
Plné texty jsou dostupné na jednotlivých ústavech Akademie věd ČR.
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, ...
On the Optimal Initial Conditions for an Inverse Problem of Model Parameter Estimation - a Complementarity Principle
Matonoha, Ctirad; Papáček, Š.
2019 - anglický
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.
Klíčová slova:
parameter identification; bleaching pattern; initial boundary value problem; sensitivity measure
Plné texty jsou dostupné v digitálním repozitáři Akademie Věd.
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 ...
Jak jsme (z)řídili ústav aneb Od Centrálního výpočetního střediska ČSAV k Ústavu informatiky AV ČR
Šebesta, Václav
2019 - český
Jak jsme (z)řídili ústav aneb Od Centrálního výpočetního střediska ČSAV k Ústavu informatiky AV ČR
Plné texty jsou dostupné v digitálním repozitáři NUŠL
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
Overdetermined Absolute Value Equations
Rohn, Jiří
2019 - anglický
We consider existence, uniqueness and computation of a solution of an absolute value equation in the overdetermined case.
Klíčová slova:
absolute value equations; overdetermined system
Plné texty jsou dostupné v digitálním repozitáři NUŠL
Overdetermined Absolute Value Equations
We consider existence, uniqueness and computation of a solution of an absolute value equation in the overdetermined case.
Generalization of a Theorem on Eigenvalues of Symmetric Matrices
Rohn, Jiří
2019 - anglický
We prove that the product of a symmetric positive semide nite matrix and a symmetric matrix has all eigenvalues real.
Klíčová slova:
symmetric matrix; positive semide nite matrix; real spectrum
Plné texty jsou dostupné v digitálním repozitáři NUŠL
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.
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