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Einmahl, John H. J.; He, Yi

Extreme value estimation for heterogeneous data. (English) Zbl 1542.62134

J. Bus. Econ. Stat. 41, No. 1, 255-269 (2023).

Cited in 2 Documents

MSC:

62P20 Applications of statistics to economics

Keywords:

extreme value theory; financial returns; heterogeneous data; power law; scales
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[1] Allen, L., Bali, T. G., and Tang, Y. (2012), “Does Systemic Risk in the Financial Sector Predict Future Economic Downturns?” The Review of Financial Studies, 25, 3000-3036. DOI: .
[2] Atkinson, A. B. (2005), “Top Incomes in the UK Over the 20th Century,” Journal of the Royal Statistical Society, Series A, 168, 325-343. DOI: . · Zbl 1114.91343
[3] Axtell, R. L. (2001), “Zipf Distribution of U.S. Firm Sizes,” Science, 293, 1818-1820. DOI: .
[4] Balkema, A. A., and de Haan, L. (1974), “Residual Life Time at Great Age,” The Annals of Probability, 2, 792-804. DOI: . · Zbl 0295.60014
[5] Barabási, A. L., and Albert, R. (1999), “Emergence of Scaling in Random Networks,” Science, 286, 509-512. DOI: . · Zbl 1226.05223
[6] Barro, R. J., and Jin, T. (2011), “On the Size Distribution of Macroeconomic Disasters,” Econometrica, 79, 1567-1589. · Zbl 1258.91177
[7] Bollerslev, T., and Wooldridge, J. M. (1992), “Quasi-Maximum Likelihood Estimation and Inference in Dynamic Models with Time-Varying Covariances,” Econometric Reviews, 11, 143-172. DOI: . · Zbl 0850.62884
[8] Cao, W., and Zhang, Z. (2020), “New Extreme Value Theory for Maxima of Maxima,” Statistical Theory and Related Fields, DOI: .
[9] Chang, L. C. (1955), “On the Ratio of the Empirical Distribution Function to the Theoretical Distribution Function,”Acta Mathematica Sinica, 347-368; English translation: Selected Translations in Mathematical Statistics and Probability, vol. 4, American Mathematical Society, 1964, 17-38. · Zbl 0202.48801
[10] Clauset, A., Shalizi, C., and Newman, M. (2009), “Power-Law Distributions in Empirical Data,” SIAM Review, 51, 661-703. DOI: . · Zbl 1176.62001
[11] Cont, R. (2001), “Empirical Properties of Asset Returns: Stylized Facts and Statistical Issues,” Quantitative Finance, 1, 223-236. DOI: . · Zbl 1408.62174
[12] di Giovanni, J., and Levchenko, A.A. (2012), “Country Size, International Trade, and Aggregate Fluctuations in Granular Economies,” Journal of Political Economy, 120, 1083-1132. DOI: .
[13] di Giovanni, J., Levchenko, A. A., and Rancière, R. (2011), “Power Laws in Firm Size and Openness to Trade: Measurement and Implications,” Journal of International Economics, 85, 42-52. DOI: .
[14] Einmahl, J. H. J., de Haan, L., and Zhou, C. (2016), “Statistics of Heteroscedastic Extremes,” Journal of the Royal Statistical Society, Series B, 78, 31-51. DOI: . · Zbl 1411.62124
[15] Embrechts, P., Klüppelberg, C., and Mikosch, T. (1997), Modelling Extremal Events: for Insurance and Finance, Berlin: Springer. · Zbl 0873.62116
[16] Fagereng, A., Guiso, L. and Pistaferri, L. (2020), “Heterogeneity and Persistence in Returns to Wealth,” Econometrica, 88, 115-170. DOI: . · Zbl 1466.91218
[17] Fama, E.F. (1963), “Mandelbrot and the Stable Paretian Hypothesis,” The Journal of Business, 36, 420-429. DOI: .
[18] Feller, W. (1978), An Introduction to Probability Theory and Its Applications, Vol. 2, New York: Wiley.
[19] Fisher, R. A., and Tippett, L.H.C. (1928), “Limiting Forms of the Frequency Distribution of the Largest or Smallest Member of a Sample,” Mathematical Proceedings of the Cambridge Philosophical Society, 24, 180-190. DOI: . · JFM 54.0560.05
[20] Fisk, P. R. (1961), “The Graduation of Income Distributions,” Econometrica, 29, 171-185. DOI: . · Zbl 0104.38702
[21] Gabaix, X. (1999), “Zipf’s Law for Cities: An Explanation,” Quarterly Journal of Economics, 114, 739-767. DOI: . · Zbl 0952.91059
[22] Gabaix, X. (2009), “Power Laws in Economics and Finance,” Annual Review of Economics, 1, 255-294.
[23] Gabaix, X. (2016), “Power Laws in Economics: An Introduction,” Journal of Economic Perspectives, 30, 185-206.
[24] Gabaix, X., Gopikrishnan, P., Plerou, V., and Stanley, H. E., “Institutional Investors and Stock Market Volatility,” The Quarterly Journal of Economics, 121, 461-504. DOI: . · Zbl 1179.91265
[25] Gabaix, X., and Ioannides, Y. M. (2004), “The Evolution of City Size Distributions,” in Handbook of Regional and Urban Economics (Vol. 4), eds. Henderson, V. and Thisse, J.-F., Amsterdam: Elsevier North-Holland, pp. 2341-2378.
[26] Gabaix, X., and Landier, A. (2008) “Why Has CEO Pay Increased so Much?” Quarterly Journal of Economics, 123, 49-100. DOI: . · Zbl 1179.91192
[27] Gabaix, X., Lasry, J. M., Lions, P. L., and Moll, B. (2016), “The Dynamics of Inequality,” Econometrica, 84, 2071-2111. DOI: . · Zbl 1420.91061
[28] Gardes, L. (2015), “A General Estimator for the Extreme Value Index: Applications to Conditional and Heteroscedastic Extremes,” Extremes, 18, 479-510. DOI: . · Zbl 1327.62207
[29] Gnedenko, B. (1943), “Sur La Distribution Limite Du Terme Maximum D’Une Série Aléatoire,” Annals of Mathematics, 44, 423-453. DOI: . · Zbl 0063.01643
[30] Gopikrishnan, P., Plerou, V., Gabaix, X., and Stanley, H. E. (2000), “Statistical Properties of Share Volume Traded in Financial Markets,” Physical Review E, 62, R4493-R4496. DOI: .
[31] Gopikrishnan, P., Plerou, V., Nunes Amaral, L. A., Meyer, M., and Stanley, H. E. (1999), “Scaling Of the Distribution of Fluctuations of Financial Market Indices,” Physical Review E, 60, 5305-5316. DOI: .
[32] de Haan, L., and Ferreira, A. (2006), Extreme Value Theory: An Introduction, New York: Springer. · Zbl 1101.62002
[33] Hill, B.M. (1975), “A Simple General Approach to Inference about the Tail of a Distribution,” The Annals of Statistics, 3, 1163-1174. DOI: . · Zbl 0323.62033
[34] Hüsler, J. (1986), “Extreme Values of Non-stationary Random Sequences,” Journal of Applied Probability, 23, 937-950. DOI: . · Zbl 0614.60021
[35] Jackson, M.O. (2009), “Networks and Economic Behavior,” Annual Review of Economics, 1, 489-511. DOI: .
[36] Jansen, D. W., and de Vries, C. G. (1991), “On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective,” The Review of Economics and Statistics, 73, 18-24. DOI: .
[37] Jessen, A. H., and Mikosch, T. (2006), “Regularly Varying Functions,” Publications de l’Institut Mathematique, 80, 171-192. DOI: . · Zbl 1164.60301
[38] Kelly, B. (2014), “The Dynamic Power Law Model,” Extremes, 17, 557-583. DOI: . · Zbl 1311.62175
[39] Kelly, B., and Jiang, H. (2014), “Tail Risk and Asset Prices,” The Review of Financial Studies, 27, 2841-2871. DOI: .
[40] Kyle, A.S., and Obizhaeva, A. A. (2016), “Market Microstructure Invariance: Empirical Hypotheses,” Econometrica, 84, 1345-1404. DOI: . · Zbl 1420.91421
[41] Leadbetter, M.R., Lindgren, G., and Rootzén, H. (1983), Extremes and Related Properties of Random Sequences and Processes, New York: Springer. · Zbl 0518.60021
[42] Longin, F.M. (1996), “The Asymptotic Distribution of Extreme Stock Market Returns,” The Journal of Business, 69, 383-408. DOI: .
[43] Mandelbrot, B. (1963), “The Variation of Certain Speculative Prices,” The Journal of Business, 36, 394-419. DOI: .
[44] Newman, M. E., Barabási, A. L. E., and Watts, D. J. (2006), The Structure and Dynamics of Networks, Princeton, NJ: Princeton University Press. · Zbl 1362.00042
[45] Pareto, V. (1896), Cours d’Économie Politique, Lausanne: F. Rouge.
[46] Pickands, J. (1975), “Statistical Inference Using Extreme Order Statistics,” The Annals of Statistics, 3, 119-131. · Zbl 0312.62038
[47] Piketty, T., and Goldhammer, A. (2014), Capital in the Twenty-First Century, Cambridge, MA: Harvard University Press.
[48] Piketty, T., and Saez, E. (2003), “Income Inequality in the United States,” Quarterly Journal of Economics, 118, 1-41. DOI: .
[49] Plerou, V., and Stanley, H. E. (2007), “Tests of Scaling and Universality of the Distributions of Trade Size and Share Volume: Evidence from Three Distinct Markets,” Physical Review E, 76, 046109. DOI: .
[50] Potter, H. (1942), “The Mean Values of Certain DIrichlet Series, II,” Proceedings of the London Mathematical Society, 2, 1-19. DOI: .
[51] Redner, S. (1998), “How Popular Is Your Paper? An Empirical Study of the Citation Distribution,” The European Physical Journal B-Condensed Matter and Complex Systems, 4, 131-134. DOI: .
[52] Resnick, S. I. (2007), Heavy-tail Phenomena: Probabilistic and Statistical Modeling, New York: Springer. · Zbl 1152.62029
[53] Schluter, C. (2021), “On Zipf’s Law and the Bias of Zipf Regressions,” Empirical Economics, 61, 529-548. DOI: .
[54] Stanley, M. H., Buldyrev, S. V., Havlin, S., Mantegna, R. N., Salinger, M. A., and Eugene Stanley, H. (1995), “Zipf Plots and the Size Distribution of Firms,” Economics Letters, 49, 453-457. DOI: . · Zbl 1058.91568
[55] Toda, A. A., and Walsh, K. (2015), “The Double Power Law in Consumption and Implications For Testing Euler Equations”, Journal of Political Economy, 123, 1177-1200. DOI: .
[56] Wellner, J. A.(1978), “Limit Theorems for the Ratio of the Empirical Distribution Function to the True Distribution Function,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 45, 73-88. DOI: . · Zbl 0382.60031
[57] Zipf, G. K. (1949), Human Behavior and the Principle of Least Effort, Boston, MA: Addison Wesley Press
[58] Zucman, G. (2019), “Global Wealth Inequality,” Annual Review of Economics, 11, 109-138. DOI: .
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