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The Asymptotic Distributions of Statistics arising in Certain Non-Parametric Tests
Glasgow mathematical journal, Tome 2 (1954) no. 1, pp. 47-51

Voir la notice de l'article provenant de la source Cambridge University Press

In a previous paper [5] the equivalence of randomisation and normal theory distributions of linear combinations was discussed. In the present paper we discuss the asymptotic randomisation distributions of statistics used in analysis of variance and in a closely related problem which includes, in particular, the “problem of m-rankings“. Kruskal [4] has studied the first of these questions in the case where observations are replaced by ranks. 
Silvey, Samuel D. The Asymptotic Distributions of Statistics arising in Certain Non-Parametric Tests. Glasgow mathematical journal, Tome 2 (1954) no. 1, pp. 47-51. doi: 10.1017/S2040618500032998
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[(1)] (1)Cramer, H., “Random variables and probability distributions,” Cambridge Tracts in Math. 36, (1937), p. 101. Google Scholar

[(2)] (2)Hoeffding, W., “A combinatorial central limit theorem,” Ann. Math. Stats., 22, 4 (1951). Google Scholar | DOI

[(3)] (3)Kendall, M. G., Advanced theory of statistics (3rd ed., London, 1947), p. 411. Google Scholar

[(4)] (4)Kruskal, W. H., “A non-parametric test for the several sample problem,” Ann. Math. Stats., 23, 4 (1952.). Google Scholar | DOI

(5) Silvey, S. D., “The equivalence of asymptotic distributions under randomisation and normal theories,” Proc. Glasgow Math. Ass., 1, 3 (1953). Google Scholar

[(6)] (6)Wald, A., and Wolfowitz, J., “Statistical tests based on permutations of the observations,” Ann. Math. Stats., 15, 4, (1944). Google Scholar | DOI

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