Jan Ámos Víšek - Academia.edu (original) (raw)
Papers by Jan Ámos Víšek
Kybernetika, 1983
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Kybernetika, 2006
The consistency of the least trimmed squares estimator (see Rousseeuw [Rous] or Hampel et al. [Ha... more The consistency of the least trimmed squares estimator (see Rousseeuw [Rous] or Hampel et al. [HamRonRouSta]) is proved under general conditions. The assumptions employed in paper are discussed in details to clarify the consequences for the applications.
Theoretical and Applied Statistics, 2019
The paper studies S-weighted estimator - a combination of S-estimator and the least weighted squa... more The paper studies S-weighted estimator - a combination of S-estimator and the least weighted squares. The estimator allows to adjust the properties, namely the level of robustness of estimator in question to the processed data better than the S-estimator or the least weighted squares can do. The paper offers the proof of its \(\sqrt{n}\)-consistency.
Advances and applications in statistics, 2015
It is shown that in the absence of spontaneous symmetry breaking the Dirac cones in the system of... more It is shown that in the absence of spontaneous symmetry breaking the Dirac cones in the system of interacting electrons on honeycomb lattice are isotropic at low energies. The effect is due to the Z3 subgroup of the D3 symmetry group of the dispersion relation of Dirac quasiparticles. Consequences of the violations of the Z3 or the sublattice symmetry are discussed.
Trabajos de Estadistica, 1991
Communications in Statistics. Part C: Sequential Analysis, 1983
In a framework of testing statistical hypotheses the sensitivity of the test error probabilities ... more In a framework of testing statistical hypotheses the sensitivity of the test error probabilities is studied. The Edgeworth approximations of proposed characteristics of this sensitivity are derived and specialized for the local alternative setting. Results, similar to Stein's lemma and Chernoff's theorem, describing the convergence rate of test risk sensitivity characteristic is given, too. An admissible character of contamination is
Journal of Statistical Planning and Inference, 1986
Abstract Characteristics of sensitivity of test error probabilities with respect to changes of un... more Abstract Characteristics of sensitivity of test error probabilities with respect to changes of underlying probability model are proposed. Explicit expressions for these characteristics are derived in the framework of a model in which a family of composite hypothese is determined by a family of capacities. Earlier results are shown to be special cases of these general ones. Also, a numerical illustration is presented.
Annals of the Institute of Statistical Mathematics, 1996
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Annals of the Institute of Statistical Mathematics, 2007
A robust version of method of Instrumental Variables accommodating the idea of an implicit weight... more A robust version of method of Instrumental Variables accommodating the idea of an implicit weighting the residuals is proposed and its properties studied. Firstly, it is shown that all solutions of the corresponding normal equations are bounded in probability. Then the weak consistency of them is proved. The algorithm, evaluating the estimate, is described and results of small MC study discussed. Keywords Robustness • Instrumental variables • Implicit weighting • Consistency of estimate by instrumental weighted variables
Bulletin of the Czech Econometric Society, 1999
Consistency, asymptotic representation and asymptotic normality of the least trimmed squares esti... more Consistency, asymptotic representation and asymptotic normality of the least trimmed squares estimator of regression coefficients is derived in the framework with random carriers. Also a result describing sensitivity to the deletion of an observation is given.
Research Papers in Economics, 2007
The robust version of the classical instrumental variables, called Instrumental Weighted Variable... more The robust version of the classical instrumental variables, called Instrumental Weighted Variables (IWV) and the conditions for its square root of n-consistency as given in the Part I and II of this paper are recalled. Of course, the reasons why the classical instrumental variables as well as IWV were introduced and the idea of implicit weighting the residuals (firstly employed by the Least Weighted Squares, see Visek (2000)) are also very briefly recalled (details were discussed in Part I of this paper). Then asymptotic representation and normality of all solutions of the corresponding normal equations is proved.
Bulletin of the Czech Econometric Society, 2002
The consistency and the asymptotic normality of the least weighted squares is proved and its asym... more The consistency and the asymptotic normality of the least weighted squares is proved and its asymptotic representation derived. Although the proof includes rather large amount of technicalities, it is not difficult to follow. The technique as follows from the analogy with the least trimmed squares will allow to study also the sensitivity of estimator to the influential points. The assumptions employed in paper as well as the properties as the scale- and regression-equivariance of the estimators are discussed. Since the paper is mostly technical, please pay attention to the Conclusions (in Part II), mainly.
Bulletin of the Czech Econometric Society, 2002
The consistency and the asymptotic normality of the least weighted squares is proved and its asym... more The consistency and the asymptotic normality of the least weighted squares is proved and its asymptotic representation derived. Although the proof includes rather large amount of technicalities, it is not difficult to follow. The technique as follows from the analogy with the least trimmed squares will allow to study also the sensitivity of estimator to the influential points. The results and the properties of the estimator are discussed in the Conclusions at the end of paper.
Condition of identifiability of linear regression model with symmetric distribution of errors is ... more Condition of identifiability of linear regression model with symmetric distribution of errors is given. Following Beran's approach for location case consistency and asymptotic normality of this adaptive estimator is proved. The result shows that the estimator is not asymptotically efficient. But it selects model with such distribution function of errors which is (in the sense of Hellinger distance applied on F(x) and 1-F(-x)) "as much as possible symmetric" which may be useful when we know that there are no reasons for the asymmetry.
Paper recalls motivation for generalized method of moments (GMM) as well as the idea estimated ge... more Paper recalls motivation for generalized method of moments (GMM) as well as the idea estimated generalized method of moments. Having demonstrated the danger of underrating the heteroscedasticity of disturbances and recalling Cragg's idea of improvement of estimation under heteroscedasticity, it offers a robustified version of it. Then it explains idea of implicit weighting of residuals, i. e. the idea of weighting of order statistics of squared residuals and outlines a modification of the least weighted squares resistant to heteroscedasticity. A proposal of robust version of GMM estimation concludes the paper.
An estimator of the contamination level of data is proposed in the framework of linear models and... more An estimator of the contamination level of data is proposed in the framework of linear models and its asymptotic behavior is investigated. A numerical study illustrates its finite sample performance under an alternative
Bulletin of the Czech Econometric Society, 1996
The result of Clemen (1986) shows that the combination of unbiased forecasts by means of a LS-reg... more The result of Clemen (1986) shows that the combination of unbiased forecasts by means of a LS-regression model without an intercept and with the constraint that coefficients sum to one gives less spread prediction than the general regression model. Here the result is generalized for the M -estimators of the regression model. In order to achieve this an asymptotic representation of the M -estimators is used.
Kybernetika, 1983
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Kybernetika, 2006
The consistency of the least trimmed squares estimator (see Rousseeuw [Rous] or Hampel et al. [Ha... more The consistency of the least trimmed squares estimator (see Rousseeuw [Rous] or Hampel et al. [HamRonRouSta]) is proved under general conditions. The assumptions employed in paper are discussed in details to clarify the consequences for the applications.
Theoretical and Applied Statistics, 2019
The paper studies S-weighted estimator - a combination of S-estimator and the least weighted squa... more The paper studies S-weighted estimator - a combination of S-estimator and the least weighted squares. The estimator allows to adjust the properties, namely the level of robustness of estimator in question to the processed data better than the S-estimator or the least weighted squares can do. The paper offers the proof of its \(\sqrt{n}\)-consistency.
Advances and applications in statistics, 2015
It is shown that in the absence of spontaneous symmetry breaking the Dirac cones in the system of... more It is shown that in the absence of spontaneous symmetry breaking the Dirac cones in the system of interacting electrons on honeycomb lattice are isotropic at low energies. The effect is due to the Z3 subgroup of the D3 symmetry group of the dispersion relation of Dirac quasiparticles. Consequences of the violations of the Z3 or the sublattice symmetry are discussed.
Trabajos de Estadistica, 1991
Communications in Statistics. Part C: Sequential Analysis, 1983
In a framework of testing statistical hypotheses the sensitivity of the test error probabilities ... more In a framework of testing statistical hypotheses the sensitivity of the test error probabilities is studied. The Edgeworth approximations of proposed characteristics of this sensitivity are derived and specialized for the local alternative setting. Results, similar to Stein's lemma and Chernoff's theorem, describing the convergence rate of test risk sensitivity characteristic is given, too. An admissible character of contamination is
Journal of Statistical Planning and Inference, 1986
Abstract Characteristics of sensitivity of test error probabilities with respect to changes of un... more Abstract Characteristics of sensitivity of test error probabilities with respect to changes of underlying probability model are proposed. Explicit expressions for these characteristics are derived in the framework of a model in which a family of composite hypothese is determined by a family of capacities. Earlier results are shown to be special cases of these general ones. Also, a numerical illustration is presented.
Annals of the Institute of Statistical Mathematics, 1996
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Annals of the Institute of Statistical Mathematics, 2007
A robust version of method of Instrumental Variables accommodating the idea of an implicit weight... more A robust version of method of Instrumental Variables accommodating the idea of an implicit weighting the residuals is proposed and its properties studied. Firstly, it is shown that all solutions of the corresponding normal equations are bounded in probability. Then the weak consistency of them is proved. The algorithm, evaluating the estimate, is described and results of small MC study discussed. Keywords Robustness • Instrumental variables • Implicit weighting • Consistency of estimate by instrumental weighted variables
Bulletin of the Czech Econometric Society, 1999
Consistency, asymptotic representation and asymptotic normality of the least trimmed squares esti... more Consistency, asymptotic representation and asymptotic normality of the least trimmed squares estimator of regression coefficients is derived in the framework with random carriers. Also a result describing sensitivity to the deletion of an observation is given.
Research Papers in Economics, 2007
The robust version of the classical instrumental variables, called Instrumental Weighted Variable... more The robust version of the classical instrumental variables, called Instrumental Weighted Variables (IWV) and the conditions for its square root of n-consistency as given in the Part I and II of this paper are recalled. Of course, the reasons why the classical instrumental variables as well as IWV were introduced and the idea of implicit weighting the residuals (firstly employed by the Least Weighted Squares, see Visek (2000)) are also very briefly recalled (details were discussed in Part I of this paper). Then asymptotic representation and normality of all solutions of the corresponding normal equations is proved.
Bulletin of the Czech Econometric Society, 2002
The consistency and the asymptotic normality of the least weighted squares is proved and its asym... more The consistency and the asymptotic normality of the least weighted squares is proved and its asymptotic representation derived. Although the proof includes rather large amount of technicalities, it is not difficult to follow. The technique as follows from the analogy with the least trimmed squares will allow to study also the sensitivity of estimator to the influential points. The assumptions employed in paper as well as the properties as the scale- and regression-equivariance of the estimators are discussed. Since the paper is mostly technical, please pay attention to the Conclusions (in Part II), mainly.
Bulletin of the Czech Econometric Society, 2002
The consistency and the asymptotic normality of the least weighted squares is proved and its asym... more The consistency and the asymptotic normality of the least weighted squares is proved and its asymptotic representation derived. Although the proof includes rather large amount of technicalities, it is not difficult to follow. The technique as follows from the analogy with the least trimmed squares will allow to study also the sensitivity of estimator to the influential points. The results and the properties of the estimator are discussed in the Conclusions at the end of paper.
Condition of identifiability of linear regression model with symmetric distribution of errors is ... more Condition of identifiability of linear regression model with symmetric distribution of errors is given. Following Beran's approach for location case consistency and asymptotic normality of this adaptive estimator is proved. The result shows that the estimator is not asymptotically efficient. But it selects model with such distribution function of errors which is (in the sense of Hellinger distance applied on F(x) and 1-F(-x)) "as much as possible symmetric" which may be useful when we know that there are no reasons for the asymmetry.
Paper recalls motivation for generalized method of moments (GMM) as well as the idea estimated ge... more Paper recalls motivation for generalized method of moments (GMM) as well as the idea estimated generalized method of moments. Having demonstrated the danger of underrating the heteroscedasticity of disturbances and recalling Cragg's idea of improvement of estimation under heteroscedasticity, it offers a robustified version of it. Then it explains idea of implicit weighting of residuals, i. e. the idea of weighting of order statistics of squared residuals and outlines a modification of the least weighted squares resistant to heteroscedasticity. A proposal of robust version of GMM estimation concludes the paper.
An estimator of the contamination level of data is proposed in the framework of linear models and... more An estimator of the contamination level of data is proposed in the framework of linear models and its asymptotic behavior is investigated. A numerical study illustrates its finite sample performance under an alternative
Bulletin of the Czech Econometric Society, 1996
The result of Clemen (1986) shows that the combination of unbiased forecasts by means of a LS-reg... more The result of Clemen (1986) shows that the combination of unbiased forecasts by means of a LS-regression model without an intercept and with the constraint that coefficients sum to one gives less spread prediction than the general regression model. Here the result is generalized for the M -estimators of the regression model. In order to achieve this an asymptotic representation of the M -estimators is used.