In this paper, we introduce the  probabilistic normed groups. Among other results, we investigate the continuityof inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. We also study midconvex functions defined  on probabilistic normed groups and  give  some results about locally boundedness of such  functions.

BACKGROUND Treatment by covariate interactions can be explored in reviews using interaction analyses (e.g., subgroup analysis). Such analyses can provide information on how the covariate modifies the treatment effect and is an important methodological approach for personalising medicine. Guidance exists regarding how to apply such analyses but little is known about whether authors follow the gu...

Abstract Isotonic distributional regression (IDR) is a powerful non-parametric technique for the estimation of conditional distributions under order restrictions. In nutshell, IDR learns that are calibrated, and simultaneously optimal relative to comprehensive classes relevant loss functions, subject isotonicity constraints in terms partial on covariate space. Non-parametric isotonic quantile b...

Time-dependent Cox regression and landmarking are the two most commonly used approaches for the analysis of time-dependent covariates in time-to-event data. The estimated effect of the time-dependent covariate in a landmarking analysis is based on the value of the time-dependent covariate at the landmark time point, after which the time-dependent covariate may change value. In this note we deri...

A fundamental task in the analysis of datasets with many variables is screening for associations. This can be cast as a multiple testing task, where objective achieving high detection power while controlling type I error. We consider $m$ hypothesis tests represented by pairs $((P_i, X_i))_{1\leq i \leq m}$ p-values $P_i$ and covariates $X_i$, such that $P_i \perp X_i$ if $H_i$ null. Here, we sh...