Generalized Probability-Probability Plots

We introduce generalized Probability-Probability (P-P) plots in order to study the one-sample goodness-of-fit problem and the two-sample problem, for real valued data.These plots, that are constructed by indexing with the class of closed intervals, globally preserve the properties of classical P-P plots and are distribution-free under the null hypothesis.We also define the generalized P-P plot process and the corresponding, consistent tests.The behaviour of the tests under contiguous alternatives is studied in detail; in particular, limit theorems for the generalized P-P plot processes are presented.By their structure, the tests perform very well for spike (or pulse) alternatives.We also study the finite sample properties of the tests through a simulation study.probability theory;limit theorems

Small nonparametric tolerance regions

We present a new natural way to construct nonparametric multivariate tolerance regions. Unlike the classical nonparametric tolerance intervals, where the endpoints of the tolerance intervals are determined by beforehand chosen order statistics, we take the shortest interval, that contains a certain number of observations. We extend this idea to higher dimensions by replacing the class of intervals with other classes of sets, like ellipsoids, hyperrectangles or convex sets. The asymptotic behaviour of our tolerance regions is derived using empirical process theory, in particular the concept of generalized quantiles. Finite sample properties of our tolerance regions are investigated through a simulation study

Generalized Probability-Probability Plots

We introduce generalized Probability-Probability (P-P) plots in order to study the one-sample goodness-of-fit problem and the two-sample problem, for real valued data.These plots, that are constructed by indexing with the class of closed intervals, globally preserve the properties of classical P-P plots and are distribution-free under the null hypothesis.We also define the generalized P-P plot process and the corresponding, consistent tests.The behaviour of the tests under contiguous alternatives is studied in detail; in particular, limit theorems for the generalized P-P plot processes are presented.By their structure, the tests perform very well for spike (or pulse) alternatives.We also study the finite sample properties of the tests through a simulation study

On nonparametric predictive inference and abjective Bayesianism

This paper consists of three main parts. First, we give an introduction to Hill’s assumption A (n) and to theory of interval probability, and an overview of recently developed theory and methods for nonparametric predictive inference (NPI), which is based on A (n) and uses interval probability to quantify uncertainty. Thereafter, we illustrate NPI by introducing a variation to the assumption A (n), suitable for inference based on circular data, with applications to several data sets from the literature. This includes attention to comparison of two groups of circular data, and to grouped data. We briefly discuss such inference for multiple future observations. We end the paper with a discussion of NPI and objective Bayesianism