Divergence from, and Convergence to, Uniformity of Probability Density Quantiles

The probability density quantile (pdQ) carries essential information regarding shape and tail behavior of a location-scale family. Convergence of repeated applications of the pdQ mapping to the uniform distribution is investigated and new fixed point theorems are established. The Kullback-Leibler divergences from uniformity of these pdQs are mapped and found to be ingredients in power functions of optimal tests for uniformity against alternative shapes.Comment: 13 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1605.0018

Conditionally Optimal Weights of Evidence

Abstract : A weight of evidence is a calibrated statistic whose values in [0, 1] indicate the degree of agreement between the data and either of two hypothesis, one being treated as the null (H 0) and the other as the alternative (H 1). A value of zero means perfect agreement with the null, whereas a value of one means perfect agreement with the alternative. The optimality we consider is minimal mean squared error (MSE) under the alternative while keeping the MSE under the null below a fixed bound. This paper studies such statistics from a conditional point of view, in particular for location and scale model