Showing papers by "Peter J. Brockwell published in 1981"
TL;DR: In this article, a class of univariate rank tests based on multiresponse permutation procedures is introduced, and asymptotic equivalence is established between one member of this class and the Kruskal-Wallis test.
Abstract: SUMMARY A class of univariate rank tests based on multiresponse permutation procedures is introduced. Asymptotic equivalence is established between one member of this class and the Kruskal-Wallis test. Simulated power comparisons for location shift detection indicate that another member of the class provides superior detection efficiency for location shifts of bimodal distributions and of heavy tailed unimodal distributions. Furthermore, both tests possess substantial computational advantages over other members of the class.
106 citations
TL;DR: In this article, 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).
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 .
27 citations