Abstract: We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models. Random-effects models and variance components estimation are classical topics in statistics, with a corresponding well-established asymptotic theory. ...

Let W ( ) be either the number of descents or inversions of a permutation 2 Sn. Stein's method is applied to bound the sup-norm distance between the distribution of W and the standard normal distribution. This appears to be the rst use of Stein's method in theory of permutation statistics. The construction of an exchangeable pair (W;W 0) used in Stein's method is non-trivial and may be of indep...