References

We investigate the rate of convergence in the multivariate CLT for sums of valued random vectors with a certain type of dependency structure, so called decompos-able random vectors, introduced by Barbour, Karoński and Ruciński (1989). This con-cept is particularly useful in random combinatorial structures, such as random graphs, random permutations, occupancy problems (bins and balls) etc. In order to derive bounds in the CLT for this type of random vectors, one can apply Stein's method (see Stein (1986)). In Barbour, Karoński and Ruciński (1989), the error in the CLT is estimated in terms of smooth test functions. In the present talk, we investigate bounds of the BerryEsseen type. Typically, if is a sum of not too dependent random vectors with and fffi ffifl, one can derive the following bound