Exact tests and confidence sets for the tail coefficient of a-stable distributions
In this paper, using the Monte Carlo (MC) method we propose an estimation and (at the same time) a test procedure for the stability parameter of a-stable distributions. One powerful advantage of the MC method is that it provides an exact significance level for finite samples, whose distribution can be far different from that of asymptotic samples on which the level of confidence interval for estimates is usually based. Statistical theory for the MC method is given. A simulation study compares the efficiency of our estimate with the Hill estimate (Hill, 1975). Construction of significance level based on the MC method is exploited and the corresponding power function is also studied. An empirical application demonstrates an easy implementation of our estimation and test procedure. It turns out that our estimate can improve the efficiency of any estimator for a in terms of mean square error.
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- McCulloch, J Huston, 1997. "Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 74-81, January.
- Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
- Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
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