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Multiple comparisons and sums of dissociated random variables. (English) Zbl 0559.60027
Let $$\{X_ I,I\in D\}$$ be a dissociated family of random variables with finite variance [cf. W. G. McGinley and R. Sibson, Math. Proc. Camb. Philos. Soc. 77, 185-188 (1975; Zbl 0353.60018)], where D denotes a collection of k-subsets of $$\{$$ 1,2,...,n$$\}$$. A Lyapunov estimate for the distance, in a suitable metric, between the distribution of $$\sum_{I\in D}X_ I$$ and the normal distribution with the same mean and variance is derived, using Stein’s method [cf. L. H. Y. Chen, Z. Wahrscheinlichkeitstheor. Verw. Geb. 43, 223-243 (1978; Zbl 0364.60049)]. The result is used to establish normal approximations for some k-sample test statistics, and in certain graph colouring problems.

##### MSC:
 60F05 Central limit and other weak theorems 62H20 Measures of association (correlation, canonical correlation, etc.) 62E20 Asymptotic distribution theory in statistics 05C15 Coloring of graphs and hypergraphs
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