Asymptotics of the sample coefficient of variation and the sample dispersion

Journal of Statistical Planning and Inference

Volumn 140, Issue 2, 2010, Pages 358-368

  Albrecher, H ^a   Ladoucette, Sophie A ^b,c   Teugels, Jef L ^b,d  

^a UNIVERSITY OF LAUSANNE   (Switzerland)

^b UNIVERSITY OF LEUVEN   (Belgium)

^c Secura   (Belgium)

^d EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Domain of attraction of a stable law; Extreme value theory; Functions of regular variation; Sample coefficient of variation; Sample dispersion; Student's t statistic; Weak limit theorems

Indexed keywords

EID: 70350412808     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2009.03.026     Document Type: Article

References (48)

1. Albrecher H., and Teugels J.L. Asymptotic analysis of a measure of variation. Theory Probab. Math. Statist. 74 (2006) 1-9
2. Araujo A., and Giné E. The Central Limit Theorem for Real and Banach Valued Random Variables (1980), Wiley, Chichester
3. Beirlant, J., Joossens, E., Segers, J., 2004a. Discussion of "Generalized Pareto fit to the society of actuaries' large claims database" by Cebrián, A., Denuit, M., Lambert, P. N. Am. Actuar. J. 8 (2), 108-111.
4. Beirlant J., Matthys G., and Dierckx G. Heavy-tailed distributions rating. Astin Bull. 31 1 (2001) 37-58
5. Beirlant J., Goegebeur Y., Segers J., and Teugels J.L. Statistics of Extremes: Theory and Applications (2004), Wiley, Chichester
6. Bennett B. On multivariate coefficients of variation. Statist. Hefte 18 2 (1977) 123-128
7. Bingham N.H., Goldie C.M., and Teugels J.L. Regular Variation. Encyclopedia of Mathematics and its Applications, vol. 27 (1987), Cambridge University Press, Cambridge
8. Caers J., Beirlant J., and Maes M.A. Statistics for modelling heavy tailed distributions in geology: part I. Methodology. Math. Geol. 31 4 (1999) 391-410
9. Charmpis, D.C., Schueller, G.I., 2004. Coping with physical uncertainties in structural mechanics: uncertainties modeling, methods of analysis and applications. Technical Report, University of Innsbruck, Austria.
10. Chistyakov G.P., and Götze F. Limit distributions of studentized means. Ann. Probab. 32 1A (2004) 28-77
11. Csörgo{combining double acute accent} M., and Horváth L. Asymptotic representations of self-normalized sums. Probab. Math. Statist. 9 1 (1988) 15-24
12. Dacorogna, M.M., Rüttener, E., 2006. Why time-diversified equalisation reserves are something worth having. Converium Research Report, Switzerland.
13. David F. Note on the application of Fisher's k-statistics. Biometrika 36 3/4 (1949) 383-393
14. Efron B. Student's t-test under symmetry conditions. J. Amer. Statist. Assoc. 64 (1969) 1278-1302
15. Feng J., and Brown D. Spike output jitter, mean firing time and coefficient of variation. J. Phys. A Math. Gen. 31 4 (1998) 1239-1252
16. Gerber H.U., and Shiu E.S.W. On the merger of two companies. N. Amer. Actuarial J. 10 3 (2006) 60-67
17. Giné E., Götze F., and Mason D.M. When is the student t-statistic asymptotically standard normal?. Ann. Probab. 25 3 (1997) 1514-1531
18. Griffin P.S., and Mason D.M. On the asymptotic normality of self-normalized sums. Math. Proc. Camb. Philos. Soc. 109 3 (1991) 597-610
19. Guillaume D.M., Dacorogna M.M., Davé R.R., Müller U.A., Olsen R.B., and Pictet O.V. From the bird's eye to the microscope: a survey of new stylized facts of the intra-day foreign exchange markets. Finance Stoch. 1 2 (1997) 95-129
20. Hájek M., and Hekera P. Can seasonal variation in fen water chemistry influence the reliability of vegetation-environment analyses?. Preslia 76 (2004) 1-14
21. Hogg R.V., and Klugman S.A. Loss Distributions (1984), Wiley, New York
22. Hong H.P., and Jiang J. Ratio between peak inelastic and elastic responses with uncertain structural properties. Canad. J. Civ. Eng. 31 4 (2004) 703-711
23. Hürlimann W. A uniform approximation to the sampling distribution of the coefficient of variation. Statist. Probab. Lett. 24 3 (1995) 263-268
24. Kaas R., Goovaerts M., Dhaene J., and Denuit M. Modern Actuarial Risk Theory (2001), Kluwer Academic Publishers, Boston
25. Knight J., and Satchell S. A re-examination of Sharpe's ratio for log-normal prices. Appl. Math. Finance 12 1 (2005) 87-100
26. Kordonsky K.B., and Gertsbakh I. Multiple time scales and the lifetime coefficient of variation: engineering applications. Lifetime Data Anal. 3 2 (1997) 139-156
27. Landsman Z. Sample quantiles and additive statistics: information, sufficiency, estimation. J. Statist. Plann. Inference 52 1 (1996) 93-108
28. Leland, W.E., Taqqu, M.S., Willinger, W., Wilson, D.V., 1993. Statistical analysis of high time-resolution ethernet LAN traffic measurements. In: Tarter, M.E., Lock, M.D. (Eds.), Proceedings of the 25th Symposium on the Interface between Statistics and Computer Science, pp. 146-155.
29. Leland W.E., Taqqu M.S., Willinger W., and Wilson D.V. On the self-similar nature of Ethernet traffic (extended version). IEEE/ACM Trans. Networking 2 (1994) 1-15
30. Li J., and Meerkov S.M. On the coefficients of variation of uptime and downtime in manufacturing equipment. Math. Probab. Eng. 2005 1 (2005) 1-6
31. Logan B.F., Mallows C.L., Rice S.O., and Shepp L.A. Limit distributions of self-normalized sums. Ann. Probab. 1 5 (1973) 788-809
32. Longin F.M. The asymptotic distribution of extreme stock market returns. J. Busin 69 3 (1996) 383-408
33. Loretan M., and Phillips P.C.B. Testing the covariance stationarity of heavy-tailed time series: an overview of the theory with applications to several financial datasets. J. Empi. Finance 1 2 (1994) 211-248
34. Mack T. Schadenversicherungsmathematik (1997), Verlag Versicherungswirtschaft e.v, Karlsruhe
35. Marrison C. The Fundamentals of Risk Measurement (2002), McGraw-Hill, New York
36. Mason D.M., and Zinn J. When does a randomly weighted self-normalized sum converge in distribution?. Electron Commun. Probab. 10 (2005) 70-81
37. Maesono, Y., 2003. Mean squared errors of ratio statistics and bias corrections. Research Report SRR03-002, Australian National University.
38. Resnick S. Heavy tail modeling and teletraffic data. Ann. Statist. 25 5 (1997) 1805-1869
39. Resnick S., and Rootzén H. Self-similar communication models and very heavy tails. Ann. Appl. Probab. 10 3 (2000) 753-778
40. Rachev, S.T., Huber, I., Ortobelli, S., 2004. Portfolio choice with heavy tailed distributions. Technical Report, University of Karlsruhe, Germany.
41. Sharpe W.F. Mutual fund performance. J. Business 39 1/2 (1966) 119-138
42. Summers R.D. An inequality for the sample coefficient of variation and an application to variables sampling. Technometrics 7 (1965) 67-68
43. Seyler C., Hofstetter T.B., and Hungerbuhler K. Life cycle inventory for thermal treatment of waste solvent from chemical industry: a multi-input allocation model. J. Cleaner Prod. 13 13/14 (2005) 1211-1224
44. Svensson G.P., Hickman M.O., Bartram S., Boland W., Pellmyr O., and Raguso R.A. Chemistry and geographic variation of floral scent in Yucca filamentosa (Agavaceae). Am. J. Bot. 92 10 (2005) 1624-1631
45. Vangel M. Confidence intervals for a normal coefficient of variation. Amer. Statist. 50 1 (1996) 21-26
46. Willinger W., Taqqu M.S., Leland W.E., and Wilson D.V. Self-similarity in highspeed packet traffic: analysis and modelling of ethernet traffic measurements. Statist. Sci. 10 1 (1995) 67-85
47. Willinger W., Taqqu M.S., Leland W.E., and Wilson D.V. Self-similarity through high variability: statistical analysis of ethernet LAN traffic at the source level extended version. IEEE/ACM Trans. Networking 51 (1997) 71-96
48. Wong A., and Wu J. Small sample asymptotic inference for the coefficient of variation: normal and nonnormal models. J. Statist. Plann. Inference 104 1 (2002) 73-82