论文信息 - High-Efficiency Estimation for the Positive Stable Laws

High-Efficiency Estimation for the Positive Stable Laws

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 Cramer-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 1 X and e 2-t 2 X .

B. M. Brown | Peter J. Brockwell | P. Brockwell | B. Brown

[1] S. J. Press,et al. Stable Distributions: Probability, Inference, and Applications in Finance—A Survey, and a Review of Recent Results , 1975 .

[2] W. DuMouchel. On the Asymptotic Normality of the Maximum-Likelihood Estimate when Sampling from a Stable Distribution , 1973 .

[3] Alois Kufner. Fourier Series , 1971 .

[4] W. DuMouchel. Stable Distributions in Statistical Inference: 2. Information from Stably Distributed Samples , 1975 .

[5] Efficiency and estimation in asymptotically normal distributions , 1973 .

[6] S. James Press,et al. Estimation in Univariate and Multivariate Stable Distributions , 1972 .

[7] A. Paulson,et al. The estimation of the parameters of the stable laws , 1975 .

[8] P. Brockwell,et al. ESTIMATION FOR THE POSITIVE STABLE LAWS, I , 1979 .

[9] B. M. Brown,et al. Expansions for the positive stable laws , 1978 .

[10] P. A. P. Moran,et al. An introduction to probability theory , 1968 .