Rates of convergence for the distance between distribution function estimators
The content of the paper is accurately given in the author's summary: ''The normed difference between ''kernel'' distribution function estimators \(\hat F{}_ n\) and the empirical distribution function \(F_ n\) is investigated. Conditions on the kernel and bandwidth of \(\hat F{}_ n\) are given so that \(a_ n\| \hat F_ n-F_ n\| \to 0\) with probability 1 as \(n\to \infty\) for both the sup-norm \(\| g\|_{\infty}=\sup | g(x)|\) and \(L_ 1\) norm \(\| g\|_ 1=\int | g(x)| dx\). Applications include equivalence in asymptotic distribution of \(T(\hat F_ n)\) and \(T(F_ n)\) (to order \(a_ n)\) for certain robust functionals T(.).''
scientific article; zbMATH DE number 3976096