Some results for locally dependent arrays (Q2737505)

The paper under review studies the empirical process of a triangular array \(X_{n,1}, \dots,X_{n,n}\), \(n\geq 1\), of \(m\)-dependent \([0,1]\)-valued random variables where \(m=m(n)=o(n)\). Some general results concerning convergence of the empirical process in \(D[0,1]\) are reviewed. For triangular arrays of the kind \(X_{n,i}= \sum^m_{k=-m} a_k\varepsilon_{i-k}\), \(i=1,\dots,n\), arising as \(m\)-dependent approximations to the linear processes \(X_i= \sum^\infty_{k= -\infty} a_k\varepsilon_{i-k}\), the criteria for convergence in \(D[0,1]\) are not satisfied. In this case, \(L^2[0,1]\)-convergence can be established.