Simple consistent estimators of stable distribution parameters

Communications in Statistics - Simulation and Computation

Volumn 15, Issue 4, 1986, Pages 1109-1136

  McCulloch, J Huston ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

asymptotic efficiency; Fama Roll method; leptorurtosis; Paretian tail; quantile estimator; skewness

Indexed keywords

EID: 38049084243     PISSN: 03610918     EISSN: 15324141     Source Type: Journal    
DOI: 10.1080/03610918608812563     Document Type: Article

References (29)

1. Arad, Ruth W. (1980). “Parameter estimation for symmetric stable distributions.” Int. Econ. Rev. 21, 209–20.
2. Bergström Harald (1952). “On some expansions of stable distribution functions,” Arkiv für Matematik 2, 375–388.
3. Brockwell, P.J. and Brown, B.M. (1981). “High-Efficiency Estimation for the Positive Stable Laws,” J. Amer. Statist. Assoc. 76, 626–631.
4. Chambers, J.M., Mallows, C.L. and Stuck, B.W. (1976). “A method for simulating stable random variables.” J. Amer. Statist. Assoc. 71, 340–4.
5. DuMouchel, William H. (1971). Stable Distributions in Statistical Inference. Unpublished Ph.D. dissertation, Yale University.
6. DuMouchel, William H. (1975). “Stable distributions in statistical inference: 2. information from stably distributed samples.” J. Amer. Statist. Assoc. 70, 386–93.
7. Fama, Eugene F. and Roll, Richard (1968). “Some properties of symmetric stable distributions.” J. Amer. Statist. Assoc. 63, 817–36.
8. Fama, Eugene F. and Roll, Richard (1971). “Parameter estimates for symmetric stable distributions.” J. Amer. Statist. Assoc. 66, 331–8.
9. Feller, William (1966). An Introduction to Probability Theory and Its Applications, Vol. II. New York: John Wiley and Sons.
10. Feuerverger, Andrey and McDunnough, Philip (1981). “On efficient inference in symmetric stable laws and processes,” Statistics and Related Topics (M. Csörgö, D.A. Dawson, J.N.K. Rao and A.K.Md.E. Saleh, Eds.). Amsterdam: North-Holland.
11. Fieletz, B.D. and Smith, E.W. (1972). “Asymmetric stable distributions of stock price changes.” J. Amer. Statist. Assoc. 67, 813–4.
12. Gnedenko, B.V. and Kolmogorov, A.N. (1968). Limit Distributions for Sums of Independent Random Variables, revised ed. Reading, Mass.: Addison-Wesley. Original Russian edition, 1948.
13. Goldberger, Arthur S. (1964). Econometric Theory. New York; John Wiley and Sons.
14. Hall, Peter (1981). “A comedy of errors: The canonical form for a stable characteristic function.” Bull. London Math. Soc. 13, 23–7.
15. Holt, Donald R. and Crow, Edwin L. (1973). “Tables and graphs of the stable probability density functions.” J. Res. Nat. Bur. Stand. 77B, 143–98.
16. Kendall, M.G. and Stuart, A. (1958). The Advanced Theory of Statistics, Vol. I - Distribution Theory. London: Charles Griffin & Co.
17. Koutrouvelis, Ioannis A. (1980). “Regression-type estimation of the parameters of stable laws.” J. Amer. Statist. Assoc. 75, 918–28.
18. Koutrouvelis, Ioannis A. (1981). “An iterative procedure for the estimation of the parameters of stable laws.” Commun. Statist.-Simula. Computa. B10, 17–28.
19. Leitch, R.A. and Paulson, A.S. (1975). “Estimation of stable law parameters: Stock price behavior application.” J. Amer. Statist. Assoc. 70, 670–7.
20. McCulloch, J. Huston (1979). “Linear regression with symmetric stable disturbances.” Ohio State University Working Paper No. 63.
21. McCulloch, J. Huston (1980). “The distribution of Student's t statistic under symmetric stable laws: A Monte Carlo sketch.” Unpublished working paper.
22. Paulson, A.S., Holcomb, E.W. and Leitch, R.A. (1975). “The estimation of the parameters of the stable laws.” Biometrika 62, 163–70.
23. Paulson, A.S., and Delahanty, T.A. (1985). “Modified weighted squared error estimation procedures with special emphasis on the stable laws,” Commun. Statis.-Simula. Computa. 14, 927–72.
24. Press, S.J. (1972). “Estimation in univariate and multivariate stable distributions.” J. Amer. Statis. Assoc. 67, 842–46.
25. So, Yuk-Chow (Jackie) (1982), The Stable Paretian Distribution of Foreign Exchange Rate Movement, Nonstationarity and Martingale: An Empirical Analysis, Unpublished Ph.D. dissertation, Ohio State University.
26. Zolotarev, Vladimir M. (1957). “Mellin-Stieltjes transforms in probability theory,” Theory of Probability and Its Application 2, 433–60.
27. Zolotarev, Vladimir M. (1966). “On representation of stable laws by integrals,” Selected Translations in Mathematical Statistics and Probability, Vol. 6. Providence: Am. Mathematical Soc., 84–8. Russian original, 1964.
28. Zolotarev, Vladimir M. (1980). “Statistical estimates of the parameters of stable laws,” Mathematical Statistics: Banach Center Publications, Vol. 6. Warsaw: Polish Scientific Publishers, 359–76.
29. Zolotarev, Vladimir M. (1983). ОД НОМЕРНЫЕ УСТОИЧИВЫЕ РАСПRЕДЕЛЕНИЯ. Moscow: T.B.M.C. English translation, One Dimensional Stable Laws, in press, Amer. Math. Soc.