Extreme Value Estimation for Heterogeneous Data

References

• 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: 10.1093/rfs/hhs094.
   Web of Science ®Google Scholar
• 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: 10.1111/j.1467-985X.2005.00351.x.
   Web of Science ®Google Scholar
• Axtell, R. L. (2001), “Zipf Distribution of U.S. Firm Sizes,” Science, 293, 1818–1820. DOI: 10.1126/science.1062081.
   PubMed Web of Science ®Google Scholar
• Balkema, A. A., and de Haan, L. (1974), “Residual Life Time at Great Age,” The Annals of Probability, 2, 792–804. DOI: 10.1214/aop/1176996548.
   Web of Science ®Google Scholar
• Barabási, A. L., and Albert, R. (1999), “Emergence of Scaling in Random Networks,” Science, 286, 509–512. DOI: 10.1126/science.286.5439.509.
   PubMed Web of Science ®Google Scholar
• Barro, R. J., and Jin, T. (2011), “On the Size Distribution of Macroeconomic Disasters,” Econometrica, 79, 1567–1589.
   Web of Science ®Google Scholar
• 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: 10.1080/07474939208800229.
   Google Scholar
• Cao, W., and Zhang, Z. (2020), “New Extreme Value Theory for Maxima of Maxima,” Statistical Theory and Related Fields, DOI: 10.1080/24754269.2020.1846115.
   Google Scholar
• 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.
   Google Scholar
• Clauset, A., Shalizi, C., and Newman, M. (2009), “Power-Law Distributions in Empirical Data,” SIAM Review, 51, 661–703. DOI: 10.1137/070710111.
   Web of Science ®Google Scholar
• Cont, R. (2001), “Empirical Properties of Asset Returns: Stylized Facts and Statistical Issues,” Quantitative Finance, 1, 223–236. DOI: 10.1080/713665670.
   Web of Science ®Google Scholar
• 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: 10.1086/669161.
   Web of Science ®Google Scholar
• 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: 10.1016/j.jinteco.2011.05.003.
   Web of Science ®Google Scholar
• 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: 10.1111/rssb.12099.
   Google Scholar
• Embrechts, P., Klüppelberg, C., and Mikosch, T. (1997), Modelling Extremal Events: for Insurance and Finance, Berlin: Springer.
   Google Scholar
• Fagereng, A., Guiso, L. and Pistaferri, L. (2020), “Heterogeneity and Persistence in Returns to Wealth,” Econometrica, 88, 115–170. DOI: 10.3982/ECTA14835.
   Web of Science ®Google Scholar
• Fama, E.F. (1963), “Mandelbrot and the Stable Paretian Hypothesis,” The Journal of Business, 36, 420–429. DOI: 10.1086/294633.
   Web of Science ®Google Scholar
• Feller, W. (1978), An Introduction to Probability Theory and Its Applications, Vol. 2, New York: Wiley.
   Google Scholar
• 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: 10.1017/S0305004100015681.
   Google Scholar
• Fisk, P. R. (1961), “The Graduation of Income Distributions,” Econometrica, 29, 171–185. DOI: 10.2307/1909287.
   Web of Science ®Google Scholar
• Gabaix, X. (1999), “Zipf’s Law for Cities: An Explanation,” Quarterly Journal of Economics, 114, 739–767. DOI: 10.1162/003355399556133.
   Web of Science ®Google Scholar
• Gabaix, X. (2009), “Power Laws in Economics and Finance,” Annual Review of Economics, 1, 255–294.
   Web of Science ®Google Scholar
• Gabaix, X. (2016), “Power Laws in Economics: An Introduction,” Journal of Economic Perspectives, 30, 185–206.
   Web of Science ®Google Scholar
• 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: 10.1162/qjec.2006.121.2.461.
   Web of Science ®Google Scholar
• Gabaix, X., and Ioannides, Y. M. (2004), “The Evolution of City Size Distributions,” in Handbook of Regional and Urban Economics (Vol. 4), eds. V. Henderson and J.-F. Thisse, Amsterdam: Elsevier North-Holland, pp. 2341–2378.
   Google Scholar
• Gabaix, X., and Landier, A. (2008) “Why Has CEO Pay Increased so Much?” Quarterly Journal of Economics, 123, 49–100. DOI: 10.1162/qjec.2008.123.1.49.
   Web of Science ®Google Scholar
• Gabaix, X., Lasry, J. M., Lions, P. L., and Moll, B. (2016), “The Dynamics of Inequality,” Econometrica, 84, 2071–2111. DOI: 10.3982/ECTA13569.
   Web of Science ®Google Scholar
• Gardes, L. (2015), “A General Estimator for the Extreme Value Index: Applications to Conditional and Heteroscedastic Extremes,” Extremes, 18, 479–510. DOI: 10.1007/s10687-015-0220-6.
   Web of Science ®Google Scholar
• Gnedenko, B. (1943), “Sur La Distribution Limite Du Terme Maximum D’Une Série Aléatoire,” Annals of Mathematics, 44, 423–453. DOI: 10.2307/1968974.
   Web of Science ®Google Scholar
• 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: 10.1103/physreve.62.r4493.
   PubMed Web of Science ®Google Scholar
• 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: 10.1103/PhysRevE.60.5305.
   PubMed Web of Science ®Google Scholar
• de Haan, L., and Ferreira, A. (2006), Extreme Value Theory: An Introduction, New York: Springer.
   Google Scholar
• Hill, B.M. (1975), “A Simple General Approach to Inference about the Tail of a Distribution,” The Annals of Statistics, 3, 1163–1174. DOI: 10.1214/aos/1176343247.
   Web of Science ®Google Scholar
• Hüsler, J. (1986), “Extreme Values of Non-stationary Random Sequences,” Journal of Applied Probability, 23, 937–950. DOI: 10.2307/3214467.
   Web of Science ®Google Scholar
• Jackson, M.O. (2009), “Networks and Economic Behavior,” Annual Review of Economics, 1, 489–511. DOI: 10.1146/annurev.economics.050708.143238.
   Web of Science ®Google Scholar
• 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: 10.2307/2109682.
   Web of Science ®Google Scholar
• Jessen, A. H., and Mikosch, T. (2006), “Regularly Varying Functions,” Publications de l’Institut Mathematique, 80, 171–192. DOI: 10.2298/PIM0694171J.
   Google Scholar
• Kelly, B. (2014), “The Dynamic Power Law Model,” Extremes, 17, 557–583. DOI: 10.1007/s10687-014-0193-x.
   Web of Science ®Google Scholar
• Kelly, B., and Jiang, H. (2014), “Tail Risk and Asset Prices,” The Review of Financial Studies, 27, 2841–2871. DOI: 10.1093/rfs/hhu039.
   Web of Science ®Google Scholar
• Kyle, A.S., and Obizhaeva, A. A. (2016), “Market Microstructure Invariance: Empirical Hypotheses,” Econometrica, 84, 1345–1404. DOI: 10.3982/ECTA10486.
   Web of Science ®Google Scholar
• Leadbetter, M.R., Lindgren, G., and Rootzén, H. (1983), Extremes and Related Properties of Random Sequences and Processes, New York: Springer.
   Google Scholar
• Longin, F.M. (1996), “The Asymptotic Distribution of Extreme Stock Market Returns,” The Journal of Business, 69, 383–408. DOI: 10.1086/209695.
   Web of Science ®Google Scholar
• Mandelbrot, B. (1963), “The Variation of Certain Speculative Prices,” The Journal of Business, 36, 394–419. DOI: 10.1086/294632.
   Web of Science ®Google Scholar
• Newman, M. E., Barabási, A. L. E., and Watts, D. J. (2006), The Structure and Dynamics of Networks, Princeton, NJ: Princeton University Press.
   Google Scholar
• Pareto, V. (1896), Cours d’Économie Politique, Lausanne: F. Rouge.
   Google Scholar
• Pickands, J. (1975), “Statistical Inference Using Extreme Order Statistics,” The Annals of Statistics, 3, 119–131.
   Web of Science ®Google Scholar
• Piketty, T., and Goldhammer, A. (2014), Capital in the Twenty-First Century, Cambridge, MA: Harvard University Press.
   Google Scholar
• Piketty, T., and Saez, E. (2003), “Income Inequality in the United States,” Quarterly Journal of Economics, 118, 1–41. DOI: 10.1162/00335530360535135.
   Web of Science ®Google Scholar
• 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: 10.1103/PhysRevE.76.046109.
   Web of Science ®Google Scholar
• Potter, H. (1942), “The Mean Values of Certain DIrichlet Series, II,” Proceedings of the London Mathematical Society, 2, 1–19. DOI: 10.1112/plms/s2-47.1.1.
   Google Scholar
• 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: 10.1007/s100510050359.
   Google Scholar
• Resnick, S. I. (2007), Heavy-tail Phenomena: Probabilistic and Statistical Modeling, New York: Springer.
   Google Scholar
• Schluter, C. (2021), “On Zipf’s Law and the Bias of Zipf Regressions,” Empirical Economics, 61, 529–548. DOI: 10.1007/s00181-020-01879-3.
   Web of Science ®Google Scholar
• 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: 10.1016/0165-1765(95)00696-D.
   Web of Science ®Google Scholar
• 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: 10.1086/682729.
   Web of Science ®Google Scholar
• 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: 10.1007/BF00635964.
   Web of Science ®Google Scholar
• Zipf, G. K. (1949), Human Behavior and the Principle of Least Effort, Boston, MA: Addison Wesley Press
   Google Scholar
• Zucman, G. (2019), “Global Wealth Inequality,” Annual Review of Economics, 11, 109–138. DOI: 10.1146/annurev-economics-080218-025852.
   Web of Science ®Google Scholar