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A Gini estimator for regression with autocorrelated errors

  • Ndéné Ka ORCID logo EMAIL logo and Stéphane Mussard
Published/Copyright: March 24, 2022

Abstract

The widely used Prais–Winsten technique for estimating parameters of linear regression model with serial correlation is sensitive to outliers. In this paper, an alternative method based on Gini mean difference (GMD) is proposed. A Monte Carlo simulation is used to show that the Gini estimator is more robust than the general least squares one when the data are contaminated by outliers.


Corresponding author: Ndéné Ka, Gredt, Université Alioune Diop de Bambey, BP 30, Bambey, Senegal, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

Carcea, M., and R. Serfling. 2015. “A Gini Autocovariance Function for Time Series Modeling.” Journal of Time Series Analysis 36: 817–38. https://doi.org/10.1111/jtsa.12130.Search in Google Scholar

Charpentier, A., N. Ka, S. Mussard, and O. Ndiaye. 2019. “Gini Regressions and Heteroskedasticity.” Econometrics 7 (14): 1–16. https://doi.org/10.3390/econometrics7010004.Search in Google Scholar

Daniels, H. E. 1944. “The Relation between Measures of Correlation in the Universe of Sample Permutation.” Biometrika 33: 129–35. https://doi.org/10.2307/2334112.Search in Google Scholar

Daniels, H. E. 1948. “A Property of Rank Correlation.” Biometrika 35: 416–7. https://doi.org/10.1093/biomet/35.3-4.416.Search in Google Scholar

Jaeckel, L. A. 1972. “Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals.” The Annals of Mathematical Statistics 43: 1449–58. https://doi.org/10.1214/aoms/1177692377.Search in Google Scholar

Ka, N., and S. Mussard. 2016. “ℓ1 Regressions: Gini Estimators for Fixed Effects Panel Data.” Journal of Applied Statistics 43 (8): 1436–46. https://doi.org/10.1080/02664763.2015.1103707.Search in Google Scholar

Lerman, R. I., and S. Yitzhaki. 1984. “A Note on the Calculation and Interpretation of the Gini Index.” Economics Letters 15: 363–8. https://doi.org/10.1016/0165-1765(84)90126-5.Search in Google Scholar

McKean, J. W., and T. P. Hettmansperger. 1978. “A Robust Analysis of the General Linear Model Based on One Step R-estimates.” Biometrika 65: 571–9. https://doi.org/10.1093/biomet/65.3.571.Search in Google Scholar

Mussard, S., and O. Ndiaye. 2018. “Vector Autoregressive Models: A Gini Approach.” Physica A 492: 1967–72. https://doi.org/10.1016/j.physa.2017.11.111.Search in Google Scholar

Olkin, I., and S. Yitzhaki. 1992. “Gini Regression Analysis.” International Statistical Review 60: 185–96. https://doi.org/10.2307/1403649.Search in Google Scholar

Prais, S. J., and C. B. Winsten. 1954. “Trend Estimators and Serial Correlation.” In Working paper 83. Cowles Commission.Search in Google Scholar

Schechtman, E., and S. Yitzhaki. 1987. “A Measure of Association Based on Gini’s Mean Difference.” Communications in Statistics 16: 207–31.10.1080/03610928708829359Search in Google Scholar

Schechtman, E., and S. Yitzhaki. 2003. “A Family of Correlation Coefficients Based on the Extended Gini Index.” The Journal of Economic Inequality 1 (2): 129–46. https://doi.org/10.1023/a:1026152130903.10.1023/A:1026152130903Search in Google Scholar

Serfling, R. J. 1980. Approximation Theorems of Mathematical Statistics. New York: John Wiley & Sons.10.1002/9780470316481Search in Google Scholar

Shelef, A., and E. Schechtman (2011). A Gini-based Methodology for Identifying and Analyzing Time Series with Non-normal Innovations, Also available at SSRN: https://doi.org/10.2139/ssrn.1885703.Search in Google Scholar

Shelef, A. 2016. “A Gini-Based Unit Root Test.” Computational Statistics & Data Analysis 100: 763–72. https://doi.org/10.1016/j.csda.2014.08.012.Search in Google Scholar

Stuart, A. 1954. “The Correlation between Variate-Values and Ranks in Samples from a Continuous Distributions.” British Journal of Statistical Psychology 7: 37–44. https://doi.org/10.1111/j.2044-8317.1954.tb00138.x.Search in Google Scholar

Yitzhaki, S., and P. J. Lambert. 2013. “The Relationship between the Absolute Deviation from a Quantile and Gini’s Mean Difference.” Metron 71 (2): 97–104. https://doi.org/10.1007/s40300-013-0015-y.Search in Google Scholar

Yitzhaki, S., and E. Schechtman. 2004. “The Gini Instrumental Variable, or the “double Instrumental Variable” Estimator.” Metron LXII (3): 287–313.Search in Google Scholar

Yitzhaki, S., and E. Schechtman. 2013. The Gini Methodology: A Primer on a Statistical Methodology. New York: Springer.10.1007/978-1-4614-4720-7Search in Google Scholar

Yitzhaki, S. 2003. “Gini’s Mean Difference: a Superior Measure of Variability for Non-normal Distributions.” Metron LXI (2): 285–316.10.2139/ssrn.301740Search in Google Scholar


Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/snde-2020-0134).


Received: 2020-12-20
Revised: 2022-02-21
Accepted: 2022-02-25
Published Online: 2022-03-24

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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