A weak law of large numbers for empirical measures via Stein's method (Q1897187)

Let a family of random elements on a locally compact Hausdorff space be given. The weak law for the independent family is proved by using Stein's method. The range of this method is extended. The class of new results for empirical measures is provided here. The main result is extended for various kinds of dependences. An estimate for the rate of convergence is derived in terms of a Zolotarev metric (semimetric). Two examples (a dissociated family, an immigration-death process) are studied.