Journal ArticleDOI
Bayesian Analysis of Composite Quantile Regression
TLDR
In this paper, a two-level hierarchical Bayesian model for coefficient estimation and future selection is proposed, which assumes a prior distribution that favors sparseness. But the proposed approach performs quite good in comparison to the other approaches.Abstract:
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 coefficient estimation and future selection which assumes a prior distribution that favors sparseness. An efficient Gibbs sampling algorithm is developed to update the unknown quantities from the posteriors. The proposed approach is illustrated via simulation studies and two real datasets. Results indicate that the proposed approach performs quite good in comparison to the other approaches.read more
Citations
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Journal ArticleDOI
Bayesian composite Tobit quantile regression
TL;DR: Composite quantile regression models have been shown to be effective techniques in improving the prediction accuracy [H. Zou and M. Yuan, Composite quantile regressions and the oracle model selectio... as discussed by the authors.
Journal ArticleDOI
Weighted composite quantile regression for longitudinal mixed effects models with application to AIDS studies
TL;DR: This paper develops a weighted CQR of longitudinal mixed model from a likelihood framework based on the composite asymmetric Laplace distribution (CALD) using the mixture representation of the CALD and achieves the iterative weighted least square estimators of unknown parameters via the MCEM (Monte Carlo Expectation Maximization) algorithm.
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Credit line exposure at default modelling using Bayesian mixed effect quantile regression
TL;DR: In this paper , the authors apply a Bayesian mixed effect quantile regression and find strongly varying covariate effects over the whole conditional distribution of credit conversion factors and especially between United States and Europe.
Journal ArticleDOI
Bayesian joint-quantile regression
TL;DR: A Bayesian joint-quantile regression method to borrow information across tail quantiles through a linear approximation of quantile coefficients is developed, motivated by a working likelihood linked to the asymmetric Laplace distributions.
Journal ArticleDOI
Bayesian bridge and reciprocal bridge composite quantile regression
TL;DR: In this article , two MCMC algorithms were developed for posterior inference using the normal-exponential mixture representation of the asymmetric Laplace distribution, and the Gamma prior was placed on the regularization parameter.
References
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Journal ArticleDOI
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Jianqing Fan,Runze Li +1 more
TL;DR: In this article, penalized likelihood approaches are proposed to handle variable selection problems, and it is shown that the newly proposed estimators perform as well as the oracle procedure in variable selection; namely, they work as well if the correct submodel were known.
Journal ArticleDOI
The Bayesian Lasso
Trevor Park,George Casella +1 more
TL;DR: The Lasso estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate when the regression parameters have independent Laplace (i.e., double-exponential) priors.
Journal ArticleDOI
Robust Tests for Heteroscedasticity Based on Regression Quantiles
Roger Koenker,Gilbert W. Bassett +1 more
Journal ArticleDOI
A gentle introduction to quantile regression for ecologists
TL;DR: Quantile regression is a way to estimate the conditional quantiles of a response variable distribution in the linear model that provides a more complete view of possible causal relationships between variables in ecological processes.
Journal ArticleDOI
Goodness of Fit and Related Inference Processes for Quantile Regression
Roger Koenker,José A. F. Machado +1 more
TL;DR: In this article, a goodness-of-fit process for quantile regression analogous to the conventional R2 statistic of least squares regression is introduced, and several related inference processes designed to test composite hypotheses about the combined effect of several covariates over an entire range of conditional quantile functions are also formulated.