S. Abramsab* , P. Janssenac & N. Veraverbekeaca Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat), Data Science (DSI), University of Hasselt, Diepenbeek, Belgiumb Global Health (GHI), Family Medicine Population (FAMPOP), Antwerp, Wilrijk, Belgiumc North-West University, Potchefstroom, South Africa

This paper derives several novel properties of conditional quantiles viewed as nonlinear operators. The results are organized in parallel to the usual expectation operator. We first define a τ-conditional quantile random set, relative any sigma-algebra, set solutions an optimization problem. Then, well-known unconditional quantiles, translation invariance, comonotonicity, and equivariance monot...

A method of obtaining an average reaction time distribution for a group of subjects is described. The method is particularly useful for cases in which data from many subjects are available but there are only 10-20 reaction time observations per subject cell. Essentially, reaction times for each subject are organized in ascending order, and quantiles are calculated. The quantiles are then averag...

A drop in dispersion, F -ratio like, permutation test (D) for linear quantile regression estimates (0 ≤ τ ≤ 1) had relative power ≥1 compared to quantile rank score tests (T ) for hypotheses on parameters other than the intercept. Power was compared for combinations of sample sizes (n = 20 − 300) and quantiles (τ = 0.50 − 0.99) where both tests maintained valid Type I error rates in simulations...

Much real data consists of more than one dimension, such as financial transactions (eg, price × volume) and IP network flows (eg, duration × numBytes), and capture relationships between the variables. For a single dimension, quantiles are intuitive and robust descriptors. Processing and analyzing such data, particularly in data warehouse or data streaming settings, requires similarly robust and...

• It is well-known that estimating extreme quantiles, namely, quantiles lying beyond the range of the available data, is a nontrivial problem that involves the analysis of tail behavior through the estimation of the extreme-value index. For heavy-tailed distributions, on which this paper focuses, the extreme-value index is often called the tail index and extreme quantile estimation typically in...

On the strong consistency of the kernel estimator of extreme conditional quantiles. 2014. HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouve...