A Critical Study of Usefulness of Selected Functional Classifiers in Economics

Authors

DOI:

https://doi.org/10.18778/0208-6018.347.05

Keywords:

functional classifier, functional data analysis, robust methods, economic optimism barometer

Abstract

In this paper we conduct a critical analysis of the most popular functional classifiers. Moreover, we propose a new classifier for functional data. Some robustness properties of the functional classifiers are discussed as well. We can use an approach worked out in this paper to predict the expected state of the economy from aggregated Consumer Confidence Index (CCI, measuring consumers optimism) and Industrial Price Index (IPI, reflecting a degree of optimism in industry sector) exploiting not only scalar values of the indices but also the trajectories/shapes of functions describing the indices. Thus our considerations may be helpful in constructing a better economic barometer. As far as we know, this is the first comparison of functional classifiers with respect to a criterion of their usefulness in economic applications. The main result of the paper is a presentation of how a small fraction of outliers in a training sample, which are linearly independent from the training sample, consisting of almost linearly dependent functions, corrupt all analysed classifiers.

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References

Arribas‑Gil A., Romo J. (2013), Shape Outlier Detection and Visualization for Functional Data: the Outliergram, “Biostatistics”, vol. 15, issue 4, pp. 603–619.
Google Scholar

Berlinet A., Thomas‑Agnan C. (2004), Reproducing Kernel Hilbert Spaces in Probability and Statistics, Kluwer, Dordrecht. https://doi.org/10.1007/978-1-4419-9096-9
Google Scholar

Białek J. (2012), Proposition of the general formula for price indices, “Communications in Statistics: Theory and Methods”, vol. 41, issue 5, pp. 943–952.
Google Scholar

Bosq D. (2000), Linear Processes in Function Spaces, Springer, New York. https://doi.org/10.1007/978-1-4612-1154-9
Google Scholar

Christmann A., Van Messem A. (2008), Bouligand Derivatives and Robustness of Support Vector Machines for Regression, “Journal of Machine Learning Research”, vol. 9, pp. 915–936.
Google Scholar

Christmann A., Salibian‑Barrera M., Van Aelst S. (2013), Qualitative Robustness of Bootstrap Approximations for Kernel Based Methods, [in:] C. Becker, R. Fried, S. Kuhnt (eds.), Robustness and Complex Data Structures, Springer, Berlin–Heidelberg, pp. 263–278. https://doi.org/10.1007/978-3-642-35494-6_16
Google Scholar

Cuevas A. (1988), Qualitative robustness in abstract inference, “Journal of Statistical Planning and Inference”, vol. 18, issue 3, pp. 277–289.
Google Scholar

Cuevas A., Fraiman R. (2009), On depth measures and dual statistics. A methodology for dealing with general data, “Journal of Multivariate Analysis”, vol. 100, issue 4, pp. 753–766.
Google Scholar

Cuevas A., Febrero‑Bande M., Fraiman R. (2007), Robust estimation and classification for functional data via projection‑based depth notions, “Computational Statistics”, vol. 22, issue 3, pp. 481–496.
Google Scholar

Devroye L., Gyorfi L., Lugosi G. (1996), A Probabilistic Theory of Pattern Recognition, Springer, New York. https://doi.org/10.1007/978-1-4612-0711-5
Google Scholar

Febrero‑Bande M. O., Fuente M. de la (2012), Statistical computing in functional data analysis: the R package fda.usc, “Journal of Statistical Software”, vol. 51, issue 4, pp. 1–28.
Google Scholar

Ferraty F., Vieu P. (2006), Nonparametric Functional Data Analysis: Theory and Practice, Spring‑ er, Berlin.
Google Scholar

Górecki T., Krzyśko M., Wołyński W. (2018), Independence test and canonical correlation analysis based on the alignment between kernel matrices for multivariate functional data, “Artificial Intelligence Review”, https://doi.org/10.1007/s10462-018-9666-7
Google Scholar

Górecki T., Krzyśko M., Waszak Ł., Wołyński W. (2018), Selected Statistical Methods of Data Analysis for Multivariate Functional Data, “Statistical Papers”, vol. 59, issue 1, pp. 153–182.
Google Scholar

Haykin S. (2009), Neural networks and learning machines, Prentice Hall, New Jersey.
Google Scholar

Horváth L., Kokoszka P. (2012), Inference for functional data with applications, Springer, New York. https://doi.org/10.1007/978-1-4614-3655-3
Google Scholar

Hubert M., Van Driessen K. (2004), Fast and robust discriminant analysis, “Computational Statistics & Data Analysis”, vol. 45, issue 2, pp. 301–320.
Google Scholar

Hubert M., Rousseeuw P., Segaert P. (2016), Multivariate and functional classification using depth and distance, “Advances in Data Analysis and Classification”, vol. 11, issue 3, pp. 445–466.
Google Scholar

Kosiorowski D. (2016), Dilemmas of robust analysis of economic data streams, “Journal of Mathematical Sciences”, vol. 218, issue 2, pp. 167–181.
Google Scholar

Kosiorowski D., Zawadzki Z. (2019), DepthProc: An R package for robust exploration of multidimensional economic phenomena, “Journal of Statistical Software” (forthcoming).
Google Scholar

Kosiorowski D., Mielczarek D., Rydlewski J. P. (2017), SVM classifiers for functional data in monitoring of the Internet users behavior, [in:] M. Papież, S. Śmiech (eds.), The 11th Professor A. Zeliaś International Conference on Modelling and Forecasting of Socio‑Economic Phenomena, Conference Proceedings, Zakopane, pp. 143–152.
Google Scholar

Kosiorowski D., Mielczarek D., Rydlewski J. P. (2018), New proposal of robust classifier for functional data, [in:] M. Papież, S. Śmiech (eds.), The 12th Professor A. Zeliaś International Conference on Modelling and Forecasting of Socio‑Economic Phenomena, Conference Proce‑ edings, Zakopane, pp. 200–208.
Google Scholar

Kosiorowski D., Rydlewski J. P., Snarska M. (2019), Detecting a structural change in functional time series using local Wilcoxon statistic, “Statistical Papers”, vol. 60, pp. 1677–1698, http://dx.doi.org/10.1007/s00362-017-0891-y
Google Scholar

Kosiorowski D., Rydlewski J. P., Zawadzki Z. (2018), Functional outliers detection by the example of air quality monitoring, “Statistical Review”, vol. 65, no. 1, pp. 81–98.
Google Scholar

Li J., Cuesta‑Albertos J. A., Liu R. Y. (2012), DD‑Classifier: Nonparametric Classification Procedure Based on DD‑Plot, “Journal of the American Statistical Association”, vol. 107, issue 498, pp. 737–753.
Google Scholar

OECD (2018), Consumer confidence index (CCI) (indicator), http://dx.doi.org/10.1787/46434d78-en
Google Scholar

Preda C. (2007), Regression models for functional data by reproducing kernel Hilbert spaces methods, “Journal of Statistical Planning and Inference”, vol. 137, issue 3, pp. 829–840.
Google Scholar

Ramsay J. O., Silverman B. W. (2005), Functional data analysis, Springer, Berlin.
Google Scholar

Ramsay J. O., Hooker G., Graves S. (2009), Functional data analysis with R and Matlab, Springer, New York.
Google Scholar

Schölkopf B., Smola A. J. (2002), Learning with Kernels, MIT Press, Cambridge.
Google Scholar

Steinwart I., Christmann A. (2008), Support Vector Machines, Springer, New York.
Google Scholar

Tarabelloni N. (2017), Robust Statistical Methods in Functional Data Analysis, Doctoral thesis and R package roahd, Politecnico di Milano, Milano.
Google Scholar

Vencálek O. (2013), Depth‑based Modification of the k‑nearest Neighbour Method, “SOP Transactions on Statistics and Analysis”, vol. 1, no. 2, pp. 131–138.
Google Scholar

Vencálek O., Pokotylo O. (2018), Depth‑weighted Bayes classification, “Computational Statistics and Data Analysis”, vol. 123, pp. 1–12.
Google Scholar

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Published

2020-04-03

How to Cite

Kosiorowski, D., Mielczarek, D., & Rydlewski, J. P. (2020). A Critical Study of Usefulness of Selected Functional Classifiers in Economics. Acta Universitatis Lodziensis. Folia Oeconomica, 2(347), 71–90. https://doi.org/10.18778/0208-6018.347.05

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