# Bayesian quantile regression for single-index models

@article{Hu2013BayesianQR, title={Bayesian quantile regression for single-index models}, author={Yuao Hu and Robert B. Gramacy and H. Lian}, journal={Statistics and Computing}, year={2013}, volume={23}, pages={437-454} }

Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work, we use a Gaussian process prior for the unknown nonparametric link function and a Laplace distribution on the index vector, with the latter motivated by the recent popularity of the Bayesian lasso idea. We design a Markov chain Monte Carlo algorithm for…

## 39 Citations

Bayesian quantile regression for partially linear additive models

- Mathematics, Computer ScienceStat. Comput.
- 2015

A semiparametric Bayesian estimation and model selection approach for partially linear additive models in conditional quantile regression with advantage that nonlinear, linear and zero function components can be separated automatically and simultaneously during model fitting without the need of pre-specification or parameter tuning.

Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood

- Computer Science, Mathematics
- 2016

It is demonstrated that a simple adjustment to the covariance matrix of the posterior chain leads to asymptotically valid posterior inference, and simulation results confirm that the posterior inference is an attractive alternative to other asymPTotic approximations in quantile regression, especially in the presence of censored data.

Bayesian Tobit quantile regression with single-index models

- Mathematics
- 2014

Based on the Bayesian framework of utilizing a Gaussian prior for the univariate nonparametric link function and an asymmetric Laplace distribution (ALD) for the residuals, we develop a Bayesian…

Bayesian elastic net single index quantile regression

- Mathematics
- 2017

ABSTRACT Single index model conditional quantile regression is proposed in order to overcome the dimensionality problem in nonparametric quantile regression. In the proposed method, the Bayesian…

Bayesian nonparametric modelling of the link function in the single-index model using a Bernstein–Dirichlet process prior

- Computer Science, MathematicsJournal of Statistical Computation and Simulation
- 2019

The Bernstein–Dirichlet process prior is modified to allow for an approximation of the unknown link function in the single-index model (SIM), and instead of the usual Gaussian distribution, the error term is assumed to be asymmetric Laplace distributed which increases the flexibility and robustness of the SIM.

Bayesian inference for conditional copulas using Gaussian Process single index models

- Computer ScienceComput. Stat. Data Anal.
- 2018

New Bayesian Single Index Quantile Regression Based on Uniform Scale Mixture

- Computer Science
- 2019

A new Bayesian lasso for single index quantile regression model is proposed based on a scale mixture uniform and an efficient and sampling Gibbs algorithm for posterior inference based onA uniform scale mixture representation for Laplace distribution is constructed.

Bayesian Analysis of Composite Quantile Regression

- Mathematics
- 2016

This paper introduces a Bayesian approach for composite quantile regression employing the skewed Laplace distribution for the error distribution. We use a two-level hierarchical Bayesian model for…

Posterior Consistency of Bayesian Quantile Regression Based on the Misspecified Asymmetric Laplace Density

- Computer Science
- 2013

An asymptotic justication for the widely used and em- pirically veried approach of assuming an asymmetric Laplace distribution for the response in Bayesian Quantile Regression by establishing posterior consistency and deriving the rate of convergence under the ALD misspecication.

Inference with Normal-Jeffreys Prior Distributions in Quantile Regression

- Mathematics
- 2017

Decades after its discussion in (Koenker and Bassett, 1978), quantile regression (QR) has been the topic of great practical applications in many areas: economics, ecology, biology and so on. In this…

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