On the convergence of \(U\)-statistics with stable limit distribution
Weak sufficient conditions are given to ensure the convergence of the distribution of suitably normalized \(U\)-statistics to an \(\alpha\)-stable distribution, \(1<\alpha\leq 2\). The proofs use Hoeffding's decomposition for \(U\)-statistics. For a subset of cases covered by the above result a rate of convergence is given which is of the same order as the rate obtained for similar stable limit results for sums of independent and identically distributed random variables.
Hoeffding's decomposition for \(U\)-statistics
scientific article; zbMATH DE number 168715