Tilo Wiklund

We generalise the known fact that for binomial $X_{n,k} \sim \mathrm{Bin}(n, k/n)$ one has $\inf_{k>1,n} \mathrm{P}(X_{n,k} \geq k) \geq \lim_{k \to 1+}\mathrm{P}(X_{2,k} \geq k) = 1/4$ to cover probabilities of exceeding a constant shift…

Given $n$ independent and identically distributed observations and measuring the value of obtaining an additional observation in terms of Le Cam's notion of deficiency between experiments, we show for certain types of non-parametric…

In this paper, we present a rigorous modular statistical approach for arguing safety or its insufficiency of an autonomous vehicle through a concrete illustrative example. The methodology relies on making appropriate quantitative studies of…

We give a distributed variant of an adaptive histogram estimation procedure previously developed by the first author. The procedure is based on regular pavings and is known to have numerous appealing statistical and arithmetical properties.…

The convex transform order is one way to make precise comparison between the skewness of probability distributions on the real line. We establish a simple and complete characterisation of when one Beta distribution is smaller than another…