arXiv subjects

Alexandre Moesching

Publications and source records attributed to Alexandre Moesching.

3 recordsLinked to original sources

arXiv2022

On Stochastic Orders and Total Positivity

The usual stochastic order and the likelihood ratio order between probability distributions on the real line are reviewed in full generality. In addition, for the distribution of a random pair $(X,Y)$, it is shown that the conditional distributions of $Y$, given $X = x$, are increasing in $x$ with respect to the likelihood ratio order if and only if the joint distribution of $(X,Y)$ is totally positive of order two (TP2) in a certain sense. It is also shown that these three types of constraints are stable under weak convergence, and that weak convergence of TP2 distributions implies convergence of the conditional distributions just mentioned.

math.ST↗

arXiv2020

Accelerating the pool-adjacent-violators algorithm for isotonic distributional regression

In the context of estimating stochastically ordered distribution functions, the pool-adjacent-violators algorithm (PAVA) can be modified such that the computation times are reduced substantially. This is achieved by studying the dependence of antitonic weighted least squares fits on the response vector to be approximated.

math.ST↗

arXiv2018

Active set algorithms for estimating shape-constrained density ratios

In many instances, imposing a constraint on the shape of a density is a reasonable and flexible assumption. It offers an alternative to parametric models which can be too rigid and to other nonparametric methods requiring the choice of tuning parameters. This paper treats the nonparametric estimation of log-concave or log-convex density ratios by means of active set algorithms in a unified framework. In the setting of log-concave densities, the new algorithm is similar to but substantially faster than previously considered active set methods. Log-convexity is a less common shape constraint which is described by some authors as "tail inflation". The active set method proposed here is novel in this context. As a by-product, new goodness-of-fit tests of single hypotheses are formulated and are shown to be more powerful than higher criticism tests in a simulation study.

stat.CO↗