Small sample robust testing for normality against Pareto tails

Communications in Statistics: Simulation and Computation

Volumn 41, Issue 7, 2012, Pages 1167-1194

  Stehlík, Milan ^a   Fabián, Zdeněk ^b   Střelec, Luboš ^c  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^b INSTITUTE OF COMPUTER SCIENCE   (Czech Republic)

^c MENDEL UNIVERSITY IN BRNO   (Czech Republic)

Author keywords

Consistency; Hill estimator; Location functional; Pareto tail; Power comparison; Returns; Robust tests for normality; T Hill estimator; Testing for normality

Indexed keywords

CONSISTENCY; HILL ESTIMATOR; PARETO TAIL; POWER COMPARISON; RETURNS; ROBUST TESTS; T-HILL ESTIMATOR;

FINANCIAL DATA PROCESSING; FISHER INFORMATION MATRIX; PARETO PRINCIPLE;

ESTIMATION;

EID: 84859857216     PISSN: 03610918     EISSN: 15324141     Source Type: Journal    
DOI: 10.1080/03610918.2012.625849     Document Type: Conference Paper

References (32)

1. Bera, A., Jarque, C. (1981). Efficient tests for normality, heteroskedasticity and serial independence of regression residuals: Monte Carlo evidence. Economics Letter 7:313-318.
2. Bickel, P. J., Lehmann, E. L. (1975). Descriptive statistics for nonparametric models II. location. The Annals of Statistics 3(5):1045-1069.
3. 2. Biometrika 62:243-250.
4. Brazauskas, V., Serfling, R. (2000a). Robust and efficient estimation of the tail index of a single-parameter Pareto distribution. North American Actuarial Journal 4:12-27.
5. Brazauskas, V., Serfling, R. (2000b). Robust estimation of tail parameters for two-parameter Pareto and exponential models via generalized quantile statistics. Extremes 3(3):231-249.
6. Brys, G., Hubert, M., Struyf, A. (2008). Goodness-of-fit tests based on a robust measure of skewness. Computational Statistics 23:429-442.
7. Cassela, G., Berger, R. L. (2002). Statistical Inference. 2nd ed. Duxbury Advanced Series, Belmont, CA: Thomson Learning.
8. Cowell, F. A., Victoria-Feser, M. P. (2007). Robust Lorenz curves: a semiparametric approach. Journal of Economic Inequality 5:21-35.
9. D'Agostino, R. B. (1986). Tests for normal distribution. In: D'Agostino, R. B., Shephens, M. A., eds. Goodness of Fit Techniques. New York: Marcel Dekker, pp. 367-419.
10. Davidson, R., Flachaire, E. (2007). Asymptotic and bootstrap inference for inequality and poverty measures. Journal of Econometrics 141:141-166. (Pubitemid 47422389)
11. Epps, T. W., Pulley, L. B. (1983). A test for normality based on the empirical characteristic function. Biometrika 70:723-726
12. Fabián, Z. (2001). Induced cores and their use in robust parametric estimation. Communication in Statistics-Theory and Methods 30:537-556.
13. Fabián, Z., Stehlík, M. (2008). A note on favorable estimation when data is contaminated. Communications in Dependability and Quality Management 11(4):36-43.
14. Gel, Y. R., Gastwirth, J. L. (2008). A robust modification of the Jarque Bera test of normality. Economics Letters 99:30-32.
15. Gel, Y. R., Miao, W., Gastwirth, J. L. (2007). Robust directed tests of normality against heavy-tailed alternatives. Computational Statistics-Data Analysis 51:2734-2746. (Pubitemid 44751254)
16. Hettmansperger, T. P., McKean, J. W. (1998). Robust nonparametric statistical methods. Kendalls Library of Statistics 5:37.
17. Jurečkové J. (2000). Test of tails based on extreme regression quantiles. Statistics & Probability Letters 49(1):53-61.
18. Jurečkové J., Picek, J. (2001). A class of tests on the tail index. Extremes 4(2):165-183.
19. Keilson, J., Steutel, F. W. (1974). Mixtures of distributions, moment inequalities and measures of exponentiality and normality. The Annals of Probability 2(1):112-130.
20. Locke, Ch., Spurrier, J. D. (1977). The use of U-statistics for testing normality against alternatives with both tails heavy or both tails light. Biometrika 64(3):638-640. (Pubitemid 8238550)
21. Mason, D. M. (1982). Laws of large numbers for sums of extreme values. Ann. Probab. 10:754-764.
22. Potocký, R., Stehlík, M. (2005). Analysis of pensions in the 1st pilar under the expected demographic development. Proceedings of 10th Slovak Conference on Demography, Smolenice.
23. Resnick, S. I. (2007). Heavy-Tail Phenomena. New York: Springer.
24. Saniga, E. M., Miles, J. A. (1979). Power of some standard goodness-of-fit tests of normality against asymmetric stable alternatives. Journal of the American Statistical Association 74(368):861-865.
25. Spiegelhalter, D. J. (1980). An omnibus test for normality for small samples. Biometrika 67:493-496.
26. Stehlík, M., Potocký, R., Waldl, H., Fabiá, Z. (2010). On the favourable estimation of fitting heavy tailed data. Computational Statistics 25:485-503.
27. Stigler, S. M. (1973). The asymptotic distribution of the trimmed mean. The Annals of Statistics 1(3):472-477.
28. Thadewald, T., Bunning, H. (2007). Jarque-Bera test and its competitors for testing normality - a power comparison. Journal of Applied Statistics 34(1):87-105.
29. Urzua, C. M. (1996). On the correct use of omnibus tests for normality. Economics Letters 53:247-251. (Pubitemid 126161293)
30. Vandewalle, B., Beirlant, J., Christmann, A., Hubert, M. (2007). A robust estimator for the tail index of Pareto-type distributions. Computational Statistics-Data Analysis 51:6252-6268. (Pubitemid 47161039)
31. Yu, J. (2001). Testing for a finite variance stock return distributions. In: Knight, J. L., Satchell, S. E., eds. Return Distributions in Finance. Oxford: Butterworth-Heinemann.
32. Wilcox, R. R. (2005). Introduction to Robust Estimation and Hypothesis Testing. 2nd ed. San Diego, CA: Academic Press, pp. 20-21.