High-Efficiency Estimation for the Positive Stable Laws
- 1 September 1981
- journal article
- research article
- Published by JSTOR in Journal of the American Statistical Association
- Vol. 76 (375) , 626
- https://doi.org/10.2307/2287521
Abstract
A moment method based on the sample averages of X -t and X -2t (with suitably chosen t) is suggested for estimating the index a and scale parameter c 1/α of the positive stable distribution with Laplace transform E exp(-ΛX) = exp(-cΛα). The corresponding Cramér-Rao lower bounds are computed by using a new and simple Fourier technique, which is based on an idea of Jarrett. It is found that the asymptotic efficiencies of the proposed estimators exceed .97 for all values of α between zero and .994. A comparison is made with the optimal asymptotic efficiencies attainable by using a different moment method based on e -t 1X and e 2-t 2X .Keywords
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