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A Robustified Metalearning Procedure for Regression Estimators
Kalina, Jan ; Neoral, A.
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.
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A Robustified Metalearning Procedure for Regression Estimators
Kalina, Jan ; Neoral, A.
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.
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How to down-weight observations in robust regression: A metalearning study
Kalina, Jan ; Pitra, Z.
Metalearning is becoming an increasingly important methodology for extracting knowledge from a data base of available training data sets to a new (independent) data set. The concept of metalearning is becoming popular in statistical learning and there is an increasing number of metalearning applications also in the analysis of economic data sets. Still, not much attention has been paid to its limitations and disadvantages. For this purpose, we use various linear regression estimators (including highly robust ones) over a set of 30 data sets with economic background and perform a metalearning study over them as well as over the same data sets after an artificial contamination.
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Nonparametric Bootstrap Techniques for Implicitly Weighted Robust Estimators
Kalina, Jan
The paper is devoted to highly robust statistical estimators based on implicit weighting, which have a potential to find econometric applications. Two particular methods include a robust correlation coefficient based on the least weighted squares regression and the minimum weighted covariance determinant estimator, where the latter allows to estimate the mean and covariance matrix of multivariate data. New tools are proposed allowing to test hypotheses about these robust estimators or to estimate their variance. The techniques considered in the paper include resampling approaches with or without replacement, i.e. permutation tests, bootstrap variance estimation, and bootstrap confidence intervals. The performance of the newly described tools is illustrated on numerical examples. They reveal the suitability of the robust procedures also for non-contaminated data, as their confidence intervals are not much wider compared to those for standard maximum likelihood estimators. While resampling without replacement turns out to be more suitable for hypothesis testing, bootstrapping with replacement yields reliable confidence intervals but not corresponding hypothesis tests.
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Nonparametric Bootstrap Techniques for Implicitly Weighted Robust Estimators
Kalina, Jan
The paper is devoted to highly robust statistical estimators based on implicit weighting, which have a potential to find econometric applications. Two particular methods include a robust correlation coefficient based on the least weighted squares regression and the minimum weighted covariance determinant estimator, where the latter allows to estimate the mean and covariance matrix of multivariate data. New tools are proposed allowing to test hypotheses about these robust estimators or to estimate their variance. The techniques considered in the paper include resampling approaches with or without replacement, i.e. permutation tests, bootstrap variance estimation, and bootstrap confidence intervals. The performance of the newly described tools is illustrated on numerical examples. They reveal the suitability of the robust procedures also for non-contaminated data, as their confidence intervals are not much wider compared to those for standard maximum likelihood estimators. While resampling without replacement turns out to be more suitable for hypothesis testing, bootstrapping with replacement yields reliable confidence intervals but not corresponding hypothesis tests.
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How to down-weight observations in robust regression: A metalearning study
Kalina, Jan ; Pitra, Zbyněk
Metalearning is becoming an increasingly important methodology for extracting knowledge from a data base of available training data sets to a new (independent) data set. The concept of metalearning is becoming popular in statistical learning and there is an increasing number of metalearning applications also in the analysis of economic data sets. Still, not much attention has been paid to its limitations and disadvantages. For this purpose, we use various linear regression estimators (including highly robust ones) over a set of 30 data sets with economic background and perform a metalearning study over them as well as over the same data sets after an artificial contamination. We focus on comparing the prediction performance of the least weighted squares estimator with various weighting schemes. A broader spectrum of classification methods is applied and a support vector machine turns out to yield the best results. While results of a leave-1-out cross validation are very different from results of autovalidation, we realize that metalearning is highly unstable and its results should be interpreted with care. We also focus on discussing all possible limitations of the metalearning methodology in general.
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Various Approaches to Szroeter’s Test for Regression Quantiles
Kalina, Jan ; Peštová, B.
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.
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Exact Inference In Robust Econometrics under Heteroscedasticity
Kalina, Jan ; Peštová, B.
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
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Exact Inference In Robust Econometrics under Heteroscedasticity
Kalina, Jan ; Peštová, Barbora
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
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