arXiv subjects

J. -L. Dortet-Bernadet

Publications and source records attributed to J. -L. Dortet-Bernadet.

3 recordsLinked to original sources

arXiv2017

Noncrossing simultaneous Bayesian quantile curve fitting

Bayesian simultaneous estimation of nonparametric quantile curves is a challenging problem, requiring a flexible and robust data model whilst satisfying the monotonicity or noncrossing constraints on the quantiles. This paper presents the use of the pyramid quantile regression method in the spline regression setting. In high dimensional problems, the choice of the pyramid locations becomes crucial for a robust parameter estimation. In this work we derive the optimal {pyramid locations which then allows us to propose an efficient} adaptive block-update MCMC scheme for posterior computation. Simulation studies show the proposed method provides estimates with significantly smaller errors and better empirical coverage probability when compared to existing alternative approaches. We illustrate the method with three real applications.

stat.ME↗

arXiv2017

Pyramid quantile regression

Quantile regression models provide a wide picture of the conditional distributions of the response variable by capturing the effect of the covariates at different quantile levels. In most applications, the parametric form of those conditional distributions is unknown and varies across the covariate space, so fitting the given quantile levels simultaneously without relying on parametric assumptions is crucial. In this work we propose a Bayesian model for simultaneous linear quantile regression. More specifically, we propose to model the conditional distributions by using random probability measures known as quantile pyramids. Unlike many existing approaches, our framework allows us to specify meaningful priors on the conditional distributions, whilst retaining the flexibility afforded by the nonparametric error distribution formulation. Simulation studies demonstrate the flexibility of the proposed approach in estimating diverse scenarios, generally outperforming other competitive methods. The method is particularly promising for modelling the extremal quantiles. Applications to linear splines and extreme value analysis are also explored through real data examples.

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arXiv2012

On Bayesian quantile regression curve fitting via auxiliary variables

Quantile regression has received increased attention in the statistics community in recent years. This article adapts an auxiliary variable method, commonly used in Bayesian variable selection for mean regression models, to the fitting of quantile regression curves. We focus on the fitting of regression splines, with unknown number and location of knots. We provide an efficient algorithm with Metropolis-Hastings updates whose tuning is fully automated. The method is tested on simulated and real examples and its extension to additive models is described. Finally we propose a simple postprocessing procedure to deal with the problem of the crossing of multiple separately estimated quantile curves.

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