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Statistical Method Selection Matters: Vanilla Methods in Regression May Yield Misleading Results
Kalina, Jan
The primary aim of this work is to illustrate the importance of the choice of the appropriate methods for the statistical analysis of economic data. Typically, there exist several alternative versions of common statistical methods for every statistical modeling task\nand the most habitually used (“vanilla”) versions may yield rather misleading results in nonstandard situations. Linear regression is considered here as the most fundamental econometric model. First, the analysis of a world tourism dataset is presented, where the number of international arrivals is modeled for 140 countries of the world as a response of 14 pillars (indicators) of the Travel and Tourism Competitiveness Index. Heteroscedasticity is clearly recognized in the dataset. However, the Aitken estimator, which would be the standard remedy in such a situation, is revealed here to be very inappropriate. Regression quantiles represent a much more suitable solution here. The second illustration with artificial data reveals standard regression quantiles to be unsuitable for data contaminated by outlying values. Their recently proposed robust version turns out to be much more appropriate. Both\nillustrations reveal that choosing suitable methods represent an important (and often difficult) part of the analysis of economic data.
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Statistical Method Selection Matters: Vanilla Methods in Regression May Yield Misleading Results
Kalina, Jan
The primary aim of this work is to illustrate the importance of the choice of the appropriate methods for the statistical analysis of economic data. Typically, there exist several alternative versions of common statistical methods for every statistical modeling task and the most habitually used (“vanilla”) versions may yield rather misleading results in nonstandard situations. Linear regression is considered here as the most fundamental econometric model. First, the analysis of a world tourism dataset is presented, where the number of international arrivals is modeled for 140 countries of the world as a response of 14 pillars (indicators) of the Travel and Tourism Competitiveness Index. Heteroscedasticity is clearly recognized in the dataset. However, the Aitken estimator, which would be the standard remedy in such a situation, is revealed here to be very inappropriate, regression quantiles represent a much more suitable solution here. The second illustration with artificial data reveals standard regression quantiles to be unsuitable for data contaminated by outlying values, their recently proposed robust version turns out to be much more appropriate. Both illustrations reveal that choosing suitable methods represent an important (and often difficult) part of the analysis of economic data.
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Some Robust Approaches to Reducing the Complexity of Economic Data
Kalina, Jan
The recent advent of complex (and potentially big) data in economics requires modern and effective tools for their analysis including tools for reducing the dimensionality (complexity) of the given data. This paper starts with recalling the importance of Big Data in economics and with characterizing the main categories of dimension reduction techniques. While there have already been numerous techniques for dimensionality reduction available, this work is interested in methods that are robust to the presence of outlying measurements (outliers) in the economic data. Particularly, methods based on implicit weighting assigned to individual observations are developed in this paper. As the main contribution, this paper proposes three novel robust methods of dimension reduction. One method is a dimension reduction within a robust regularized linear regression, namely a sparse version of the least weighted squares estimator. The other two methods are robust versions of feature extraction methods popular in econometrics: robust principal component analysis and robust factor analysis.
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Some Robust Approaches to Reducing the Complexity of Economic Data
Kalina, Jan
The recent advent of complex (and potentially big) data in economics requires modern and effective tools for their analysis including tools for reducing the dimensionality (complexity) of the given data. This paper starts with recalling the importance of Big Data in economics and with characterizing the main categories of dimension reduction techniques. While there have already been numerous techniques for dimensionality reduction available, this work is interested in methods that are robust to the presence of outlying measurements (outliers) in the economic data. Particularly, methods based on implicit weighting assigned to individual observations are developed in this paper. As the main contribution, this paper proposes three novel robust methods of dimension reduction. One method is a dimension reduction within a robust regularized linear regression, namely a sparse version of the least weighted squares estimator. The other two methods are robust versions of feature extraction methods popular in econometrics: robust principal component analysis and robust factor analysis.
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A Bootstrap Comparison of Robust Regression Estimators
Kalina, Jan ; Janáček, Patrik
The ordinary least squares estimator in linear regression is well known to be highly vulnerable to the presence of outliers in the data and available robust statistical estimators represent more preferable alternatives. It has been repeatedly recommended to use the least squares together with a robust estimator, where the latter is understood as a diagnostic tool for the former. In other words, only if the robust estimator yields a very different result, the user should investigate the dataset closer and search for explanations. For this purpose, a hypothesis test of equality of the means of two alternative linear regression estimators is proposed here based on nonparametric bootstrap. The performance of the test is presented on three real economic datasets with small samples. Robust estimates turn out not to be significantly different from non-robust estimates in the selected datasets. Still, robust estimation is beneficial in these datasets and the experiments illustrate one of possible ways of exploiting the bootstrap methodology in regression modeling. The bootstrap test could be easily extended to nonlinear regression models.
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On kernel-based nonlinear regression estimation
Kalina, Jan ; Vidnerová, P.
This paper is devoted to two important kernel-based tools of nonlinear regression: the Nadaraya-Watson estimator, which can be characterized as a successful statistical method in various econometric applications, and regularization networks, which represent machine learning tools very rarely used in econometric modeling. This paper recalls both approaches and describes their common features as well as differences. For the Nadaraya-Watsonestimator, we explain its connection to the conditional expectation of the response variable. Our main contribution is numerical analysis of suitable data with an economic motivation and a comparison of the two nonlinear regression tools. Our computations reveal some tools for the Nadaraya-Watson in R software to be unreliable, others not prepared for a routine usage. On the other hand, the regression modeling by means of regularization networks is much simpler and also turns out to be more reliable in our examples. These also bring unique evidence revealing the need for a careful choice of the parameters of regularization networks
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Application Of Implicitly Weighted Regression Quantiles: Analysis Of The 2018 Czech Presidential Election
Kalina, Jan ; Vidnerová, P.
Regression quantiles can be characterized as popular tools for a complex modeling of a continuous response variable conditioning on one or more given independent variables. Because they are however vulnerable to leverage points in the regression model, an alternative approach denoted as implicitly weighted regression quantiles have been proposed. The aim of current work is to apply them to the results of the second round of the 2018 presidential election in the Czech Republic. The election results are modeled as a response of 4 demographic or economic predictors over the 77 Czech counties. The analysis represents the first application of the implicitly weighted regression quantiles to data with more than one regressor. The results reveal the implicitly weighted regression quantiles to be indeed more robust with respect to leverage points compared to standard regression quantiles. If however the model does not contain leverage points, both versions of the regression quantiles yield very similar results. Thus, the election dataset serves here as an illustration of the usefulness of the implicitly weighted regression quantiles.
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Application Of Implicitly Weighted Regression Quantiles: Analysis Of The 2018 Czech Presidential Election
Kalina, Jan ; Vidnerová, Petra
Regression quantiles can be characterized as popular tools for a complex modeling of a continuous response variable conditioning on one or more given independent variables. Because they are however vulnerable to leverage points in the regression model, an alternative approach denoted as implicitly weighted regression quantiles have been proposed. The aim of current work is to apply them to the results of the second round of the 2018 presidential election in the Czech Republic. The election results are modeled as a response of 4 demographic or economic predictors over the 77 Czech counties. The analysis represents the first application of the implicitly weighted regression quantiles to data with more than one regressor. The results reveal the implicitly weighted regression quantiles to be indeed more robust with respect to leverage points compared to standard regression quantiles. If however the model does not contain leverage points, both versions of the regression quantiles yield very similar results. Thus, the election dataset serves here as an illustration of the usefulness of the implicitly weighted regression quantiles.
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On kernel-based nonlinear regression estimation
Kalina, Jan ; Vidnerová, Petra
This paper is devoted to two important kernel-based tools of nonlinear regression: the Nadaraya-Watson estimator, which can be characterized as a successful statistical method in various econometric applications, and regularization networks, which represent machine learning tools very rarely used in econometric modeling. This paper recalls both approaches and describes their common features as well as differences. For the Nadaraya-Watson estimator, we explain its connection to the conditional expectation of the response variable. Our main contribution is numerical analysis of suitable data with an economic motivation and a comparison of the two nonlinear regression tools. Our computations reveal some tools for the Nadaraya-Watson in R software to be unreliable, others not prepared for a routine usage. On the other hand, the regression modeling by means of regularization networks is much simpler and also turns out to be more reliable in our examples. These also bring unique evidence revealing the need for a careful choice of the parameters of regularization networks
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