Prague Economic Papers 2012, 21(1):69-82 | DOI: 10.18267/j.pep.411

On Multivariate Methods in Robust Econometrics

Jan Kalina
Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, CZ - 182 07, Praha 8 (kalina@cs.cas.cz).

This work studies implicitly weighted robust statistical methods suitable for econometric problems. We study robust estimation mainly for the context of heteroscedasticity or high dimension, which are up-to-date topics of current econometrics. We describe a modification of linear regression resistant to heteroscedasticity and study its computational aspects. For a robust version of the instrumental variables estimator we propose an asymptotic test of heteroscedasticity. Further we describe robust statistical methods for dimension reduction and classification analysis. We propose the robust quadratic classification analysis based on a new minimum weighted covariance determinant (MWCD) estimator. In general the robust methods based on down-weighting less reliable observations are resistant to outlying values (outliers) and insensitive to the assumption of Gaussian normal distribution of the data. The methods are illustrated on econometric data examples.

Keywords: least weighted squares, heteroscedasticity, multivariate statistics, model selection, diagnostics, computational aspects
JEL classification: C13, C14, C51

Published: January 1, 2012  Show citation

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Kalina, J. (2012). On Multivariate Methods in Robust Econometrics. Prague Economic Papers, 21(1), 69-82. doi: 10.18267/j.pep.411
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    References

    1. Aitken, A. C. (1935), "On Least Squares and Linear Combination of Observations". Proceedings of the Royal Statistical Society 55, pp. 42-48. Go to original source...
    2. Alqallaf, F.; van Aelst, S.; Yohai, V. J.; Zamar, R. H. (2009), "Propagation of Outliers in Multivariate Data." Annals of Statistics 37, No. 1, pp. 311-331. Go to original source...
    3. Čížek, P. (2008), "Efficient Robust Estimation of Time-Series Regression Models." Applications of Mathematics 53, No. 3, pp. 267-279. Go to original source...
    4. Cragg, J. G. (1983), "More Efficient Estimation in the Presence of Heteroscedasticity of Unknown Form." Econometrica 51, No. 3, pp. 751-763. Go to original source...
    5. Croux, C.; Haesbroeck, G. (2000), "Principal Component Analysis Based on Robust Estimators of the Covariance or Correlation Matrix: Influence Functions and Efficiencies." Biometrika 87, pp. 603-618. Go to original source...
    6. García-Escudero, L. A.; Gordaliza, A. (2005), "Generalized Radius Processes for Elliptically Contoured Distributions." Journal of the American Statistical Association 100, pp. 1036-1045. Go to original source...
    7. Gelper, S.; Schettlinger, K.; Croux, C.; Gather, U. (2009), "Robust Online Scale Estimation in Time Series: a Model-Free Approach." Journal of Statistical Planning and Inference 139, pp. 335-339. Go to original source...
    8. Greene, W. H. (2002), Econometric Analysis. Fifth edition. New York: Macmillan.
    9. Hansen, L. P. (1982), "Large Samples Properties of Generalized Method of Moments Estimators." Econometrica 50, No. 4, pp. 1029-1054. Go to original source...
    10. Hekimoglu, S.; Erenoglu, R. C.; Kalina, J. (2009), "Outlier Detection by Means of Robust Regression Estimators for Use in Engineering Science." Journal of Zhejiang University - Science A (JZUS-A) 10, No. 6, pp. 909-921. Go to original source...
    11. Hubert, M.; Rousseeuw, P. J.; Vanden Branden, K. (2005), "ROBPCA: A New Approach to Robust Principal Component Analysis." Technometrics 47, pp. 64-79. Go to original source...
    12. Ihaka, R.; Gentleman, R. R. (1996), "A Language for Data Analysis and Graphics." Journal of Computational and Graphical Statistics 5, pp. 299-314. Go to original source...
    13. Johnson R. A.; Wichern, D. W. (1982), Applied Multivariate Statistical Analysis. Prentice-Hall, Englewood Cliffs.
    14. Kalina, J. (2007), "Asymptotic Durbin-Watson Test for Robust Regression." Bulletin of the International Statistical Institute 62, pp. 3406-3409.
    15. Kalina, J. (2008), "Robustní regrese a diagnostické nástroje." In Kupka, K. (Ed.), Data analysis 2007/II, Progressive methods of statistical data analysis and modelling for research and technical practice. Trilobyte Statistical Software, Pardubice, pp. 31-41. (In Czech.)
    16. Kmenta, J. (1986), Elements of Econometrics. New York: Macmillan.
    17. Maddala, G. S. (1988), Introduction to Econometrics. New York: Macmillan.
    18. Riani, M.; Atkinson, A. C.; Cerioli, A. (2009), "Finding an Unknown Number of Multivariate Outliers." Journal of the Royal Statistical Society, Series B, 71, pp. 447-466. Go to original source...
    19. Ronchetti, E.; Trojani, F. (2001), "Robust Inference with GMM Estimators." Journal of econometrics 101, pp. 37-69. Go to original source...
    20. Rousseeuw, P. J.; Leroy, A. M. (1987), Robust Regression and Outlier Detection. New York: Wiley. Go to original source...
    21. Rousseeuw, P. J.; van Driessen, K. (1999), "A Fast Algorithm for the Minimum Covariance Determinant Estimator." Technometrics 41, No. 3, pp. 212-223. Go to original source...
    22. Rousseeuw, P. J.; van Driessen, K. (2006), "Computing LTS Regression for Large Data Sets." Data Mining and Knowledge Discovery 12, pp. 29-45. Go to original source...
    23. Salibián-Barrera, M.; Yohai, V. J. (2006), "A Fast Algorithm for S-Regression Estimates." Journal of Computational and Graphical Statistics 15, pp. 414-427. Go to original source...
    24. Szroeter, J. (1978), "A Class of Parametric Tests of Heteroscedasticity in Linear Econometric Models." Econometrica 46, pp. 1311-1328. Go to original source...
    25. Todorov, V.; Pires, A. M. (2007), "Comparative Performance of Several Robust Linear Discriminant Analysis Methods." REVSTAT Statistical Journal 5, pp. 63-83.
    26. Varmuza, K.; Filzmoser, P. (2009), Introduction to Multivariate Statistical Analysis in Chemometrics. Boca Raton: Taylor & Francis - CRC Press. Go to original source...
    27. Víšek, J. Á. (2001), "Regression with High Breakdown Point." In Antoch, J.; Dohnal, G. (Eds.), Proceedings of ROBUST 2000, Summer School of JČMF, JČMF and Czech Statistical Society, pp. 324-356.
    28. Víšek, J. Á. (2005), "Robustifying Generalized Method of Moments." In Kupka K. (Ed.): Data analysis 2004/II, Progressive Methods of Statistical Data Analysis and Modelling for Research and Technical Practice, Trilobyte, Pardubice, pp. 171-193.
    29. Víšek, J. Á. (2006), "Instrumental Weighted Variables." Austrian Journal of Statistics 35, No. 2&3, pp. 379-387.
    30. Wagenvoort, R.; Waldmann, R. (2002), "On B-Robust Instrumental Variable Estimation of the Linear Model with Panel Data." Journal of Econometrics 106, pp. 297-324. Go to original source...
    31. Wooldridge, J. M. (2001), "Applications of Generalized Method of Moments Estimation." Journal of Economic Perspectives 15, No. 4, pp. 87-100. Go to original source...

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