Convex rearrangements, generalized Lorenz curves, and correlated Gaussian data

Journal of Statistical Planning and Inference

Volumn 137, Issue 3, 2007, Pages 915-934

  Davydov, Youri ^a   Khoshnevisan, Davar ^b   Shi, Zhan ^c   Zitikis, Ričardas ^d  

^a UNIV LILLE   (France)

^b UNIVERSITY OF UTAH   (United States)

^c University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

^d UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

Convex rearrangements; Fractional Brownian motion; Gini indices; Lorenz curves

Indexed keywords

EID: 33751042706     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2006.06.032     Document Type: Article

References (25)

1. Bardet J.-M. Un test d'auto-similarité pour les processus gaussiens à accroissements stationnaires. C. R. Acad. Sci. Paris Sér. I Math. 328 (1999) 521-526
2. Barrett, G.F., Donald, S.G., 2002. Statistical inference with generalized Gini indices of inequality and poverty. Discussion Paper 2002/01, School of Economics, University of New South Wales.
3. Csörgo{combining double acute accent} M., and Zitikis R. On the general Bahadur-Kiefer, quantile, and Vervaat processes: old and new. In: Berkes I., Csáki E., and Csörgo{combining double acute accent} M. (Eds). Limit Theorems in Probability and Statistics I (A Volume in Honour of Pál Révész) (2002), Bolyai Mathematical Society, Budapest 389-426
4. David H.A. Gini's mean difference rediscovered. Biometrika 55 (1968) 573-575
5. Davydov Y., and Zitikis R. Generalized Lorenz curves and convexifications of stochastic processes. J. Appl. Probab. 40 (2003) 906-925
6. Dehling H., and Taqqu M.S. The empirical process of some long-range dependent sequences with an application to U-statistics. Ann. Statist. 17 (1989) 1767-1783
7. Dobrushin R.L. Describing a system of random variables by conditional distributions. Theoret. Probab. Appl. 15 (1970) 458-486
8. Gastwirth J.L. A general definition of the Lorenz curve. Econometrica 39 (1971) 1037-1039
9. Giorgi G.-M. A fresh look at the topical interest of the Gini concentration ratio. Metron 51 (1993) 83-98
10. Giorgi G.-M. Bibliographic portrait of the Gini concentration ratio. Metron 48 (1990) 183-221
11. Giraitis L., and Surgailis D. CLT and other limit theorems for functionals of Gaussian processes. Z. Wahrsch. Verw. Gebiete 70 (1985) 191-212
12. Guyon X., and León J. Convergence en loi des H-variations d'un processus gaussien stationnaire sur R. Ann. Inst. H. Poincaré Probab. Statist. 25 (1989) 265-282
13. Itô K. Multiple Wiener integral. J. Math. Soc. Japan 3 (1951) 157-164
14. Lorenz M.O. Methods of measuring the concentration of wealth. J. Amer. Statist. Assoc. 9 (1905) 209-219
15. Maruyama G. The harmonic analysis of stationary stochastic processes. Mem. Fac. Sci. Kyushu Univ., Ser. A 4 (1949) 45-106
16. Mosler, K., 2002. Multivariate Dispersion, Central Regions and Depth: The Lift Zonoid Approach. Lecture Notes in Statistics. Springer, New York.
17. Ros, A., 2001. The Isoperimetric Problem. Lecture Series at the Clay Mathematical Institute Summer School on the Global Theory of Minimal Surfaces, Summer 2001, Mathematical Science Research Institute, Berkeley, CA.
18. Rosenblatt, M., 1961. Independence and dependence. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. II. University of California Press, Berkeley, CA, pp. 431-443.
19. Shorack G.R., and Wellner J.A. Empirical Processes with Applications to Statistics (1986), Wiley, New York
20. Slepian D. The one-sided barrier problem for Gaussian noise. Bell System Tech. J. 42 1962 (1962)
21. Taqqu M.S. Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrsch. Verw. Gebiete 31 (1974/1975) 287-302
22. Taqqu M.S. Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence. Z. Wahrsch. Verw. Gebiete 40 3 (1977) 203-238
23. Zitikis R. The Vervaat process. In: Szyszkowicz B. (Ed). Asymptotic Methods in Probability and Statistics (1988), North-Holland, Amsterdam 667-694
24. Zitikis, R., 2002. Analysis of indices of economic inequality from a mathematical point of view. Lecture at the 11th Indonesian Mathematics Conference, State University of Malang, Indonesia, Matematika, vol. 8, pp. 772-782.
25. Zitikis R. Asymptotic estimation of the E-Gini index. Econometric Theory 19 (2003) 587-601