A multivariate CLT for local dependence with \(n^{-1/2}\log n\) rate and applications to multivariate graph related statistics
Let \(X_1,\dots,X_n\) be \(r\)-dimensional random vectors, and define \(W=X_1+\cdots+X_n\). This paper explores the proximity of \(W\) to the standard normal distribution by presenting upper bounds for \(\sup\{|Eh(W)-\int_{\mathbb{R}^d} h(z)\Phi(dx)|: h\in {\mathcal H}\}\), where \(\Phi\) is the standard normal distribution function on \(\mathbb{R}^d\) and \(\mathcal H\) is a class of functions from \(\mathbb{R}^d\) to \(\mathbb{R}\) which obey certain specified properties. These results are applied to statistical problems involving both random and non-random graphs.
scientific article; zbMATH DE number 892483