zbMATH — the first resource for mathematics

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.

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
Full Text: DOI