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Various Approaches to Szroeter’s Test for Regression Quantiles
Kalina, Jan; Peštová, B.
2017 - anglický
Regression quantiles represent an important tool for regression analysis popular in econometric applications, for example for the task of detecting heteroscedasticity in the data. Nevertheless, they need to be accompanied by diagnostic tools for verifying their assumptions. The paper is devoted to heteroscedasticity testing for regression quantiles, while their most important special case is commonly denoted as the regression median. Szroeter’s test, which is one of available heteroscedasticity tests for the least squares, is modified here for the regression median in three different ways: (1) asymptotic test based on the asymptotic representation for regression quantiles, (2) permutation test based on residuals, and (3) exact approximate test, which has a permutation character and represents an approximation to an exact test. All three approaches can be computed in a straightforward way and their principles can be extended also to other heteroscedasticity tests. The theoretical results are expected to be extended to other regression quantiles and mainly to multivariate quantiles.
Klíčová slova:
Heteroscedasticity; Regression median; Diagnostic tools; Asymptotics
Dokument je dostupný na externích webových stránkách.
Various Approaches to Szroeter’s Test for Regression Quantiles
Regression quantiles represent an important tool for regression analysis popular in econometric applications, for example for the task of detecting heteroscedasticity in the data. Nevertheless, they ...
Flexible Moment Invariant Bases for 2D Scalar and Vector Fields
Bujack, R.; Flusser, Jan
2017 - anglický
Complex moments have been successfully applied to pattern detection tasks in two-dimensional real, complex, and vector valued functions. In this paper, we review the different bases of rotational moment invariants based on the generator approach with complex monomials. We analyze their properties with respect to independence, completeness, and existence and\npresent superior bases that are optimal with respect to all three criteria for both scalar and vector fields.
Klíčová slova:
Pattern detection; moment invariants; scalar fields; vector fields; flow fields; generator; basis; complex; monomial
Dokument je dostupný na externích webových stránkách.
Flexible Moment Invariant Bases for 2D Scalar and Vector Fields
Complex moments have been successfully applied to pattern detection tasks in two-dimensional real, complex, and vector valued functions. In this paper, we review the different bases of rotational ...
Avoiding overfitting of models: an application to research data on the Internet videos
Jiroušek, Radim; Krejčová, I.
2017 - anglický
The problem of overfitting is studied from the perspective of information theory. In this context, data-based model learning can be viewed as a transformation process, a process transforming the information contained in data into the information represented by a model. The overfitting of a model often occurs when one considers an unnecessarily complex model, which usually means that the considered model contains more information than the original data. Thus, using one of the basic laws of information theory saying that any transformation cannot increase the amount of information, we get the basic restriction laid on models constructed from data: A model is acceptable if it does not contain more information than the input data file.
Klíčová slova:
data-based learning; probabilistic models; information theory; MDL principle; lossless encoding
Dokument je dostupný na externích webových stránkách.
Avoiding overfitting of models: an application to research data on the Internet videos
The problem of overfitting is studied from the perspective of information theory. In this context, data-based model learning can be viewed as a transformation process, a process transforming the ...
Causality and Intervention in Business Process Management
Bína, V.; Jiroušek, Radim
2017 - anglický
The paper presents an algebraic approach to the modeling of causality in systems of stochastic variables. The methodology is based on an operator of a composition that provides the possibility of composing a multidimensional distribution from low-dimensional building blocks taking advantage of the dependence structure of the problem variables. The authors formally define and demonstrate on a hypothetical example a surprisingly elegant unifying approach to conditioning by a single variable and the evaluation of the effect of an intervention. Both operations are realized by the composition with a degenerated distribution and differ only in the sequence in which the operator of the composition is performed.
Klíčová slova:
Compositional model; Operator of composition,; Causality; Conditioning; Intervention
Dokument je dostupný na externích webových stránkách.
Causality and Intervention in Business Process Management
The paper presents an algebraic approach to the modeling of causality in systems of stochastic variables. The methodology is based on an operator of a composition that provides the possibility of ...
Hidden Auto-Conflict in the Theory of Belief Functions
Daniel, M.; Kratochvíl, Václav
2017 - anglický
Hidden conflicts of belief functions in some cases where the sum of all multiples of conflicting belief masses being equal to zero were observed. Relationships of hidden conflicts and auto-conflicts of belief functions are pointed out. We are focused on hidden auto-conflicts here - on hidden conflicts appearing when three or more numerically same belief functions are combined. Hidden auto-conflict is a kind of internal conflict. Degrees of hidden auto-conflicts and full non-conflictness are defined and analysed. Finally, computational issues of hidden auto-conflicts and non-conflictness are presented.
Klíčová slova:
Belief functions; Dempster-Shafer theory; Uncertainty; Conflicting belief masses; Internal conflict; Auto-conflict; Hidden-conflict
Dokument je dostupný na externích webových stránkách.
Hidden Auto-Conflict in the Theory of Belief Functions
Hidden conflicts of belief functions in some cases where the sum of all multiples of conflicting belief masses being equal to zero were observed. Relationships of hidden conflicts and auto-conflicts ...
Exact Inference In Robust Econometrics under Heteroscedasticity
Kalina, Jan; Peštová, B.
2017 - anglický
The paper is devoted to the least weighted squares estimator, which is one of highly robust estimators for the linear regression model. Novel permutation tests of heteroscedasticity are proposed. Also the asymptotic behavior of the permutation test statistics of the Goldfeld-Quandt and Breusch-Pagan tests is investigated. A numerical experiment on real economic data is presented, which also shows how to perform a robust prediction model under heteroscedasticity. Theoretical results may be simply extended to the context of multivariate quantiles
Klíčová slova:
heteroscedasticity; robust statistics; regression; diagnostic tools; economic data
Dokument je dostupný na externích webových stránkách.
Exact Inference In Robust Econometrics under Heteroscedasticity
The paper is devoted to the least weighted squares estimator, which is one of highly robust estimators for the linear regression model. Novel permutation tests of heteroscedasticity are proposed. Also ...
A machine learning method for incomplete and imbalanced medical data
Salman, I.; Vomlel, Jiří
2017 - anglický
Our research reported in this paper is twofold. In the first part of the paper we use\nstandard statistical methods to analyze medical records of patients suffering myocardial\ninfarction from the third world Syria and a developed country - the Czech Republic.\nOne of our goals is to find whether there are statistically significant differences between\nthe two countries. In the second part of the paper we present an idea how to deal with\nincomplete and imbalanced data for tree-augmented naive Bayesian (TAN). All results\npresented in this paper are based on a real data about 603 patients from a hospital in\nthe Czech Republic and about 184 patients from two hospitals in Syria.
Klíčová slova:
Machine Learning; Data Analysis; Bayesian networks; Imbalanced Data; Acute Myocardial Infarction
Dokument je dostupný na externích webových stránkách.
A machine learning method for incomplete and imbalanced medical data
Our research reported in this paper is twofold. In the first part of the paper we use\nstandard statistical methods to analyze medical records of patients suffering myocardial\ninfarction from the ...
Optimal Value of Loans via Stochastic Programming
Kaňková, Vlasta
2017 - anglický
A question of mortgage leads to serious and complicated problems of financial mathematics. On one side is a bank with an aim to have a “good” profit, on the other side is the client trying to invest money safely, with possible “small” risk.Let us suppose that a young married couple is in a position of client. Young people know that an expected and also unexpected unpleasant financial situation can happen. Many unpleasant financial situation can be caused by a random factor. Consequently stochastic methods are suitable to secure against them. The aim of the suggested model is not only to state a maximal reasonable value of loans, but also to endure unpleasant financial period. To this end we employ stochastic optimization theory. A few suitable models will be introduced. The choice of the model depends on environment of the young people. Models will be with “deterministic” constraints, probability constraints, but also with stochastic dominance constraints. The suggested models will be analyzed both from the numerical point of view and from possible method solution based on data. Except static one-objective problem we suggest also multi–objective models.
Klíčová slova:
Loan-debtor; installments; stochastic programming; probability constraints; second order dominance constraints
Dokument je dostupný na externích webových stránkách.
Optimal Value of Loans via Stochastic Programming
A question of mortgage leads to serious and complicated problems of financial mathematics. On one side is a bank with an aim to have a “good” profit, on the other side is the client trying to invest ...
Feasibility Study of an Interactive Medical Diagnostic Wikipedia
Grim, Jiří
2016 - anglický
Considering different application possibilities of product distribution mixtures we have proposed three formal tools in the last years, which can be used to accumulate decision-making know-how from particular diagnostic cases. First, we have developed a structural mixture model to estimate multidimensional probability distributions from incomplete and possibly weighted data vectors. Second, we have shown that the estimated product mixture can be used as a knowledge base for the Probabilistic Expert System (PES) to infer conclusions from definite or even uncertain input information. Finally we have shown that, by using product mixtures, we can exactly optimize sequential decision-making by means of the Shannon formula of conditional informativity. We combine the above statistical tools in the framework of an interactive open-access medical diagnostic system with automatic accumulation of decision-making knowledge.
Klíčová slova:
Multivariate statistics; Medical diagnostics; Product mixtures; Incomplete data; Sequential classification; EM algorithm
Dokument je dostupný na externích webových stránkách.
Feasibility Study of an Interactive Medical Diagnostic Wikipedia
Considering different application possibilities of product distribution mixtures we have proposed three formal tools in the last years, which can be used to accumulate decision-making know-how from ...
Decision of a Steel Company Trading with Emissions
Zapletal, F.; Šmíd, Martin
2016 - anglický
We formulate a Mean-CVaR decision problem of a production company obliged to cover its CO2 emissions by allowances. Certain amount of the allowances is given to the company for free, the missing/redundant ones have to be bought/sold on a market. To manage their risk, the company can use derivatives on emissions allowances (in particular futures and options), in addition to spot values of allowances. We solve the decision problem for the case of an real-life Czech steel company for different levels of risk aversion and different scenarios of the demand. We show that the necessity of emissions trading generally, and the risk caused by the trading in particular, can influence the production significantly even when the risk is decreased by means of derivatives. The results of the study show that even for low levels of the risk aversion, futures on allowances are optimal to use in order to reduce the risk caused by the emissions trading.
Klíčová slova:
CVaR; emission trading; optimization; allowances; EU ETS
Dokument je dostupný na externích webových stránkách.
Decision of a Steel Company Trading with Emissions
We formulate a Mean-CVaR decision problem of a production company obliged to cover its CO2 emissions by allowances. Certain amount of the allowances is given to the company for free, the ...
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