Central limit theorem for U-statistics of associated random variables (Q1613035)

Let \(\{X_n;n\geq 1\}\) be a sequence of stationary associated random variables, that is, for every \(k\) and for every pair of \(k\)-variate functions \(h(x_1, \dots,x_k)\) and \(g(x_1, \dots,x_k)\), which are non-decreasing componentwise, \[ \text{cov} \bigl(h(X_1, \dots,X_k), g(X_1,\dots,X_k) \bigr)\geq 0 \] whenever it is finite. The authors establish a central limit theorem for U-statistics of degree two, based on the above sample, using the Hoeffding decomposition.