Robust estimation of the Pareto index: A Monte Carlo Analysis
The Pareto distribution is often used in many areas of economics to model the right tail of heavy-tailed distributions. However, the standard method of estimating the shape parameter (the Pareto index) of this distribution– the maximum likelihood estimator (MLE) – is non-robust, in the sense that it is very sensitive to extreme observations, data contamination or model deviation. In recent years, a number of robust estimators for the Pareto index have been proposed, which correct the deficiency of the MLE. However, little is known about the performance of these estimators in small-sample setting, which often occurs in practice. This paper investigates the small-sample properties of the most popular robust estimators for the Pareto index, including the optimal B-robust estimator (OBRE) (Victoria-Feser and Ronchetti, 1994, The Canadian Journal of Statistics 22: 247–258), the weighted maximum likelihood estimator (WMLE) (Dupuis and Victoria-Feser, 2006, Canadian Journal of Statistics 34: 639–658), the generalized median estimator (GME) (Brazauskas and Serfling, 2001a, Extremes 3, 231–249), the partial density component estimator (PDCE) (Vandewalle et al., 2007, Computational Statistics & Data Analysis 51: 6252–6268), and the probability integral transform statistic estimator (PITSE) (Finkelstein et al., 2006, North American Actuarial Journal 10, 1–10). Monte Carlo simulations show that the PITSE offers the desired compromise between ease of use and power to protect against outliers in the small-sample setting.
|Date of creation:||2013|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: (+48 22) 55 49 144
Fax: (+48 22) 831 28 46
Web page: http://www.wne.uw.edu.pl/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Soo, Kwok Tong, 2005.
"Zipf's Law for cities: a cross-country investigation,"
Regional Science and Urban Economics,
Elsevier, vol. 35(3), pages 239-263, May.
- Kwok Tong Soo, 2004. "Zipfs Law for Cities: A Cross Country Investigation," CEP Discussion Papers dp0641, Centre for Economic Performance, LSE.
- Kwok Tong Soo, 2004. "Zipf's law for cities: a cross country investigation," LSE Research Online Documents on Economics 19947, London School of Economics and Political Science, LSE Library.
- Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006.
"Institutional Investors and Stock Market Volatility,"
The Quarterly Journal of Economics,
MIT Press, vol. 121(2), pages 461-504, May.
- Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2005. "Institutional Investors and Stock Market Volatility," NBER Working Papers 11722, National Bureau of Economic Research, Inc.
- Xavier Gabaix & Rustam Ibragimov, 2011.
"Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents,"
Journal of Business & Economic Statistics,
Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
- Xavier Gabaix & Rustam Ibragimov, 2007. "Rank-1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents," NBER Technical Working Papers 0342, National Bureau of Economic Research, Inc.
- Mehmet A. Ulubaşoğlu & Bharat R. Hazari, 2004. "Zipf's law strikes again: the case of tourism," Journal of Economic Geography, Oxford University Press, vol. 4(4), pages 459-472, August.
- Niklas Wagner & Terry Marsh, 2004. "Tail index estimation in small smaples Simulation results for independent and ARCH-type financial return models," Statistical Papers, Springer, vol. 45(4), pages 545-561, October.
- Frank Cowell & Maria-Pia Victoria-Feser, 2007. "Robust stochastic dominance: A semi-parametric approach," Journal of Economic Inequality, Springer, vol. 5(1), pages 21-37, April.
- Michał Brzeziński, 2013.
"Relative risk aversion and power-law distribution of macroeconomic disasters,"
2013-04, Faculty of Economic Sciences, University of Warsaw.
- Michal Brzezinski, 2015. "Relative Risk Aversion and Power‐Law Distribution of Macroeconomic Disasters," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(1), pages 170-175, 01.
- Frank A. Cowell & Emmanuel Flachaire, 2004.
"Income distribution and inequality measurement : the problem of extreme values,"
Cahiers de la Maison des Sciences Economiques
v04101, Université Panthéon-Sorbonne (Paris 1).
- Cowell, Frank A. & Flachaire, Emmanuel, 2007. "Income distribution and inequality measurement: The problem of extreme values," Journal of Econometrics, Elsevier, vol. 141(2), pages 1044-1072, December.
- Frank A. Cowell & Emmanuel Flachaire, 2007. "Income distribution and inequality measurement: The problem of extreme values," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00176029, HAL.
- Xavier Gabaix, 2008.
"Power Laws in Economics and Finance,"
NBER Working Papers
14299, National Bureau of Economic Research, Inc.
- Cowell, Frank A & Victoria-Feser, Maria-Pia, 1996. "Robustness Properties of Inequality Measures," Econometrica, Econometric Society, vol. 64(1), pages 77-101, January.
- Xavier Gabaix & Augustin Landier, 2008.
"Why Has CEO Pay Increased So Much?,"
The Quarterly Journal of Economics,
MIT Press, vol. 123(1), pages 49-100, 02.
- Bellio, Ruggero, 2007. "Algorithms for bounded-influence estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2531-2541, February.
- Beran, Jan & Schell, Dieter, 2012. "On robust tail index estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3430-3443.
- Vandewalle, B. & Beirlant, J. & Christmann, A. & Hubert, M., 2007. "A robust estimator for the tail index of Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6252-6268, August.
- F. Clementi & M. Gallegati, 2004.
"Power Law Tails in the Italian Personal Income Distribution,"
- Clementi, F. & Gallegati, M., 2005. "Power law tails in the Italian personal income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 427-438.
- Fabio Clementi & Mauro Gallegati, 2005. "Power Law Tails in the Italian Personal Income Distribution," Microeconomics 0505005, EconWPA.
- Klass, Oren S. & Biham, Ofer & Levy, Moshe & Malcai, Ofer & Solomon, Sorin, 2006. "The Forbes 400 and the Pareto wealth distribution," Economics Letters, Elsevier, vol. 90(2), pages 290-295, February.
- Andreas Alfons & Matthias Templ & Peter Filzmoser, 2013. "Robust estimation of economic indicators from survey samples based on Pareto tail modelling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(2), pages 271-286, 03.
- Ramsay, Colin M., 2003. "A solution to the ruin problem for Pareto distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 109-116, August.
- Casey B. Mulligan & Andrei Shleifer, 2005. "The Extent of the Market and the Supply of Regulation," The Quarterly Journal of Economics, MIT Press, vol. 120(4), pages 1445-1473, November.
- Gaffeo, Edoardo & Gallegati, Mauro & Giulioni, Gianfranco & Palestrini, Antonio, 2003. "Power laws and macroeconomic fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 408-416.
- Jeroen Hinloopen & Charles van Marrewijk, 2012. "Power laws and comparative advantage," Applied Economics, Taylor & Francis Journals, vol. 44(12), pages 1483-1507, April.
- Tomson Ogwang, 2011. "Power laws in top wealth distributions: evidence from Canada," Empirical Economics, Springer, vol. 41(2), pages 473-486, October.
- Erzo G. J. Luttmer, 2007. "Selection, Growth, and the Size Distribution of Firms," The Quarterly Journal of Economics, MIT Press, vol. 122(3), pages 1103-1144, 08.
When requesting a correction, please mention this item's handle: RePEc:war:wpaper:2013-32. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Marcin Bąba)
If references are entirely missing, you can add them using this form.