The rate of convergence in the central limit theorem for non-stationary dependent random vectors
Let \((X_ j\), \(j\geq 1)\) be a strictly stationary sequence of uniformly mixing variables with zero mean, unit variance and finite fourth moments. Consider the vector \(S_ n=\sum^{n}_{j=1}\alpha_{nj}X_ j\) where \(\alpha_{nj}=(\alpha_{nj1}\), \(\alpha_{nj2})'\), \(\alpha_{nj1}\), \(\alpha_{nj2}\in R\) 1 and \(| \alpha_{nj1}| \leq 1,| \alpha_{nj2}| \leq 1\). The author estimates the rate at which \(S_ n\) converges to normality. The extension of this result to bounded R s- valued weights (s\(\geq 1)\) has also been indicated.
scientific article; zbMATH DE number 4054693
scientific article