5 citations · 8 across the 15 of their papers we have counts for
15 papers
Conditional bias reduction can be dangerous: a key example from sequential analysis
Ben Berckmoes, Anna Ivanova, Geert Molenberghs
We present a key example from sequential analysis, which illustrates that conditional bias reduction can cause infinite mean absolute error.
On asymptotic normality in estimation after a group sequential trial
Ben Berckmoes, Anna Ivanova, Geert Molenberghs
We prove that in many realistic cases, the ordinary sample mean after a group sequential trial is asymptotically normal if the maximal number of observations increases. We derive t…
On the sample mean after a group sequential trial
Ben Berckmoes, Anna Ivanova, Geert Molenberghs
A popular setting in medical statistics is a group sequential trial with independent and identically distributed normal outcomes, in which interim analyses of the sum of the outcom…
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 asymptotic normality and the construction of confidence intervals for estimators after sampling with probabilistic and deterministic stopping rules
Ben Berckmoes, Geert Molenberghs
A key feature of a sequential study is that the actual sample size is a random variable that typically depends on the outcomes collected. While hypothesis testing theory for sequen…
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…
A compactness result in approach theory with an application to the continuity approach structure
Ben Berckmoes
We establish a compactness result in approach theory which we apply to obtain a generalization of Prokhorov's Theorem for the continuity approach structure.
On the asymptotic behavior of the contaminated sample mean
Ben Berckmoes, Geert Molenberghs
An observation of a cumulative distribution function with finite variance is said to be contaminated according to the inflated variance model if it has a large probability of c…
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 Arzelà-Ascoli theorem for the Hausdorff measure of noncompactness
Ben Berckmoes
We generalize the Arzelà-Ascoli theorem in the space of continuous maps on a compact interval with values in Euclidean N-space by providing a quantitative link between the Hausdorf…
A uniformly continuous linear extension principle in topological vector spaces with an application to Lebesgue integration
Ben Berckmoes
We prove a uniformly continuous linear extension principle in topological vector spaces from which we derive a very short and canonical construction of the Lebesgue integral of Ban…
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…