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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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