Number of found documents: 1162
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Least Weighted Absolute Value Estimator with an Application to Investment Data
Vidnerová, Petra; Kalina, Jan
2020 - English
While linear regression represents the most fundamental model in current econometrics, the least squares (LS) estimator of its parameters is notoriously known to be vulnerable to the presence of outlying measurements (outliers) in the data. The class of M-estimators, thoroughly investigated since the groundbreaking work by Huber in 1960s, belongs to the classical robust estimation methodology (Jurečková et al., 2019). M-estimators are nevertheless not robust with respect to leverage points, which are defined as values outlying on the horizontal axis (i.e. outlying in one or more regressors). The least trimmed squares estimator seems therefore a more suitable highly robust method, i.e. with a high breakdown point (Rousseeuw & Leroy, 1987). Its version with weights implicitly assigned to individual observations, denoted as the least weighted squares estimator, was proposed and investigated in Víšek (2011). A trimmed estimator based on the 𝐿1-norm is available as the least trimmed absolute value estimator (Hawkins & Olive, 1999), which has not however acquired attention of practical econometricians. Moreover, to the best of our knowledge, its version with weights implicitly assigned to individual observations seems to be still lacking. Keywords: robust regression; regression median; implicit weighting; computational aspects; nonparametric bootstrap Fulltext is available at external website.
Least Weighted Absolute Value Estimator with an Application to Investment Data

While linear regression represents the most fundamental model in current econometrics, the least squares (LS) estimator of its parameters is notoriously known to be vulnerable to the presence of ...

Vidnerová, Petra; Kalina, Jan
Ústav informatiky, 2020

On the Effect of Human Resources on Tourist Infrastructure: New Ideas on Heteroscedastic Modeling Using Regression Quantiles
Kalina, Jan; Janáček, Patrik
2020 - English
Tourism represents an important sector of the economy in many countries around the world. In this work, we are interested in the effect of the Human Resources and Labor Market pillar of the Travel and Tourism Competitiveness Index on tourist service infrastructure across 141 countries of the world. A regression analysis requires to handle heteroscedasticity in these data, which is not an uncommon situation in various available human capital studies. Our first task is focused on testing significance of individual variables in the model. It is illustrated here that significance tests are influenced by heteroscedasticity, which remains true also for tests for regression quantiles or robust regression estimators, resistant to a possible contamination of data by outliers. Only if a suitable model is considered, which takes heteroscedasticity into account, the effect of the Human Resources and Labor Market pillar turns out to be significant. Further, we propose and present a new diagnostic tool denoted as aquintile plot, allowing to interpret immediately the heteroscedastic structure of the linear regression model for possibly contaminated data. Keywords: tourism infrastructure; human resources; regression; robustness; regression quantiles Fulltext is available at external website.
On the Effect of Human Resources on Tourist Infrastructure: New Ideas on Heteroscedastic Modeling Using Regression Quantiles

Tourism represents an important sector of the economy in many countries around the world. In this work, we are interested in the effect of the Human Resources and Labor Market pillar of the Travel and ...

Kalina, Jan; Janáček, Patrik
Ústav informatiky, 2020

Two limited-memory optimization methods with minimum violation of the previous quasi-Newton equations
Vlček, Jan; Lukšan, Ladislav
2020 - English
Limited-memory variable metric methods based on the well-known BFGS update are widely used for large scale optimization. The block version of the BFGS update, derived by Schnabel (1983), Hu and Storey (1991) and Vlček and Lukšan (2019), satisfies the quasi-Newton equations with all used difference vectors and for quadratic objective functions gives the best improvement of convergence in some sense, but the corresponding direction vectors are not descent directions generally. To guarantee the descent property of direction vectors and simultaneously violate the quasi-Newton equations as little as possible in some sense, two methods based on the block BFGS update are proposed. They can be advantageously combined with methods based on vector corrections for conjugacy (Vlček and Lukšan, 2015). Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new methods. Keywords: unconstrained minimization; variable metric methods; limited-memory methods; variationally derived methods; global convergence; numerical results Available in a digital repository NRGL
Two limited-memory optimization methods with minimum violation of the previous quasi-Newton equations

Limited-memory variable metric methods based on the well-known BFGS update are widely used for large scale optimization. The block version of the BFGS update, derived by Schnabel (1983), Hu and Storey ...

Vlček, Jan; Lukšan, Ladislav
Ústav informatiky, 2020

Linear-time Algorithms for Largest Inscribed Quadrilateral
Keikha, Vahideh
2020 - English
Let P be a convex polygon of n vertices. We present a linear-time algorithm for the problem of computing the largest-area inscribed quadrilateral of P. We also design the parallel version of the algorithm with O(log n) time and O(n) work in CREW PRAM model, which is quite work optimal. Our parallel algorithm also computes all the antipodal pairs of a convex polygon with O(log n) time and O(log2n+s) work, where s is the number of antipodal pairs, that we hope is of independent interest. We also discuss several approximation algorithms (both constant factor and approximation scheme) for computing the largest-inscribed k-gons for constant values of k, in both area and perimeter measures. Keywords: Maximum-area quadrilateral; extreme area k-gon Available in a digital repository NRGL
Linear-time Algorithms for Largest Inscribed Quadrilateral

Let P be a convex polygon of n vertices. We present a linear-time algorithm for the problem of computing the largest-area inscribed quadrilateral of P. We also design the parallel version of the ...

Keikha, Vahideh
Ústav informatiky, 2020

Regression for High-Dimensional Data: From Regularization to Deep Learning
Kalina, Jan; Vidnerová, Petra
2020 - English
Regression modeling is well known as a fundamental task in current econometrics. However, classical estimation tools for the linear regression model are not applicable to highdimensional data. Although there is not an agreement about a formal definition of high dimensional data, usually these are understood either as data with the number of variables p exceeding (possibly largely) the number of observations n, or as data with a large p in the order of (at least) thousands. In both situations, which appear in various field including econometrics, the analysis of the data is difficult due to the so-called curse of dimensionality (cf. Kalina (2013) for discussion). Compared to linear regression, nonlinear regression modeling with an unknown shape of the relationship of the response on the regressors requires even more intricate methods. Keywords: regression; neural networks; robustness; high-dimensional data; regularization Fulltext is available at external website.
Regression for High-Dimensional Data: From Regularization to Deep Learning

Regression modeling is well known as a fundamental task in current econometrics. However, classical estimation tools for the linear regression model are not applicable to highdimensional data. ...

Kalina, Jan; Vidnerová, Petra
Ústav informatiky, 2020

The Equation |x| - |Ax| = b
Rohn, Jiří
2020 - English
We formulate conditions on A and b under which the double absolute value equation |x| - |Ax| = b possesses in each orthant a unique solution which, moreover, belongs to the interior of that orthant. Keywords: absolute value equation; double absolute value equation; orthantwise solvability; theorem of the alternatives Available in a digital repository NRGL
The Equation |x| - |Ax| = b

We formulate conditions on A and b under which the double absolute value equation |x| - |Ax| = b possesses in each orthant a unique solution which, moreover, belongs to the interior of that orthant.

Rohn, Jiří
Ústav informatiky, 2020

The scalar-valued score functions of continuous probability distribution
Fabián, Zdeněk
2019 - English
In this report we give theoretical basis of probability theory of continuous random variables based on scalar valued score functions. We maintain consistently the following point of view: It is not the observed value, which is to be used in probabilistic and statistical considerations, but its 'treated form', the value of the scalar-valued score function of distribution of the assumed model. Actually, the opinion that an observed value of random variable should be 'treated' with respect to underlying model is one of main ideas of the inference based on likelihood in classical statistics. However, a vector nature of Fisher score functions of classical statistics does not enable a consistent use of this point of view. Instead, various inference functions are suggested and used in solutions of various statistical problems. Inference function of this report is the scalar-valued score function of distribution. Keywords: Shortcomings of probability theory; Scalar-valued score functions; Characteristics of continous random variables; Parametric estimation; Transformed distributions; Skew-symmetric distributions Available at various institutes of the ASCR
The scalar-valued score functions of continuous probability distribution

In this report we give theoretical basis of probability theory of continuous random variables based on scalar valued score functions. We maintain consistently the following point of view: It is not ...

Fabián, Zdeněk
Ústav informatiky, 2019

Lexicalized Syntactic Analysis by Restarting Automata
Mráz, F.; Otto, F.; Pardubská, D.; Plátek, Martin
2019 - English
We study h-lexicalized two-way restarting automata that can rewrite at most i times per cycle for some i ≥ 1 (hRLWW(i)-automata). This model is considered useful for the study of lexical (syntactic) disambiguation, which is a concept from linguistics. It is based on certain reduction patterns. We study lexical disambiguation through the formal notion of h-lexicalized syntactic analysis (hLSA). The hLSA is composed of a basic language and the corresponding h-proper language, which is obtained from the basic language by mapping all basic symbols to input symbols. We stress the sensitivity of hLSA by hRLWW(i)-automata to the size of their windows, the number of possible rewrites per cycle, and the degree of (non-)monotonicity. We introduce the concepts of contextually transparent languages (CTL) and contextually transparent lexicalized analyses based on very special reduction patterns, and we present two-dimensional hierarchies of their subclasses based on the size of windows and on the degree of synchronization. The bottoms of these hierarchies correspond to the context-free languages. CTL creates a proper subclass of context-sensitive languages with syntactically natural properties. Keywords: Restarting automaton; h-lexicalization; lexical disambiguation Fulltext is available at external website.
Lexicalized Syntactic Analysis by Restarting Automata

We study h-lexicalized two-way restarting automata that can rewrite at most i times per cycle for some i ≥ 1 (hRLWW(i)-automata). This model is considered useful for the study of lexical (syntactic) ...

Mráz, F.; Otto, F.; Pardubská, D.; Plátek, Martin
Ústav informatiky, 2019

Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator
Gergelits, Tomáš; Mardal, K.-A.; Nielsen, B. F.; Strakoš, Z.
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: second order elliptic PDEs; preconditioning by the inverse Laplacian; eigenvalues of the discretized preconditioned problem; nodal values of the coefficient function; Hall’s theorem; convergence of the conjugate gradient method Available in digital repository of the ASCR
Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator

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 ...

Gergelits, Tomáš; Mardal, K.-A.; Nielsen, B. F.; Strakoš, Z.
Ústav informatiky, 2019

A Logical Characteristic of Read-Once Branching Programs
Žák, Stanislav
2019 - English
We present a mathematical model of the intuitive notions such as the knowledge or the information arising at different stages of computations on branching programs (b.p.). The model has two appropriate properties: i) The ”knowledge” arising at a stage of computation in question is derivable from the ”knowledge” arising at the previous stage according to the rules of the model and according to the local arrangement of the b.p. ii) The model confirms the intuitively well-known fact that the knowledge arising at a node of a computation depends not only on it but in some cases also on a ”mystery” information. (I. e. different computations reaching the same node may have different knowledge(s) arisen at it.) We prove that with respect to our model no such information exists in read-once b.p.‘s but on the other hand in b. p.‘s which are not read-once such information must be present. The read-once property forms a frontier. More concretely, we may see the instances of our models as a systems S = (U,D) where U is a universe of knowledge and D are derivation rules. We say that a b.p. P is compatible with a system S iff along each computation in P S derives F (false) or T (true) at the end correctly according to the label of the reached sink. This key notion modifies the classic paradigm which takes the computational complexity with respect to different classes of restricted b.p.‘s (e.g. read-once b.p.‘s, k-b.p.‘s, b.p.‘s computing in limited time etc.). Now, the restriction is defined by a subset of systems and only these programs are taken into account which are compatible with at least one of the chosen systems. Further we understand the sets U of knowledge(s) as a sets of admissible logical formulae. It is clear that more rich sets U‘s imply the large restrictions on b.p.‘s and consequently the smaller complexities of Boolean functions are detected. More rich logical equipment implies stronger computational effectiveness. Another question arises: given a set of Boolean functions (e.g. codes of some graphs) what logical equipment is optimal from the point of complexity? Keywords: branching programs; computational complexity; logic Available in digital repository of the ASCR
A Logical Characteristic of Read-Once Branching Programs

We present a mathematical model of the intuitive notions such as the knowledge or the information arising at different stages of computations on branching programs (b.p.). The model has two ...

Žák, Stanislav
Ústav informatiky, 2019

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