5 citations · 8 across the 15 of their papers we have counts for
7 papers · 1 filter
Approximate central limit theorems
Ben Berckmoes, Geert Molenberghs
We refine the classical Lindeberg-Feller central limit theorem by obtaining asymptotic bounds on the Kolmogorov distance, the Wasserstein distance, and the parametrized Prokhorov d…
An approach theoretic version of Anscombe's theorem with an application in biostatistics
Ben Berckmoes
We establish an approach theoretic version of Anscombe's theorem, which we apply to justify the use of confidence intervals based on the sample mean after a group sequential trial.
An application of approach theory to the relative Hausdorff measure of non-compactness for the Wasserstein metric
Ben Berckmoes, Tim Hellemans, Mark Sioen +1
After shortly reviewing the fundamentals of approach theory as introduced by R. Lowen in 1989, we show that this theory is intimately related with the well-known Wasserstein metric…
On the Hausdorff measure of non-compactness for the parametrized Prokhorov metric
Ben Berckmoes
We quantify Prokhorov's Theorem by establishing an explicit formula for the Hausdorff measure of non-compactness (HMNC) for the parametrized Prokhorov metric on the set of Borel pr…
A note on probability metrics in a categorical setting
Ben Berckmoes, Bob Lowen
Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variable…
Stein's method and a quantitative Lindeberg CLT for the Fourier transforms of random vectors
Ben Berckmoes, Bob Lowen, Jan Van Casteren
We use a multivariate version of Stein's method to establish a quantitative Lindeberg CLT for the Fourier transforms of random -vectors. We achieve this by deducing a specific i…
An isometric study of the Lindeberg-Feller CLT via Stein's method
Ben Berckmoes, Bob Lowen, Jan Van Casteren
We use Stein's method to prove a generalization of the Lindeberg-Feller CLT providing an upper and a lower bound for the superior limit of the Kolmogorov distance between a normall…