Bayesian quantile regression for single-index models

Abstract

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 posterior inference. Careful consideration of the singularity of the kernel matrix, and tractability of some of the full conditional distributions leads to a partially collapsed approach where the nonparametric link function is integrated out in some of the sampling steps. Our simulations demonstrate the superior performance of the Bayesian method versus the frequentist approach. The method is further illustrated by an application to the hurricane data.

Semiparametric quantile estimation for varying coefficient partially linear measurement errors models

“…For the estimation problem and statistical inference of semiparametric quantile regression (SQR), there is much work in the literature. See, for example, Cai and Xiao (2012); Fan and Zhu (2013); Hu et al (2013); Wang, Zhu and Zhou (2009). Recently, Kai et al (2011) proposed an SQR procedure when the conditional quantile of the response-given covariates is modeled as PLVCMs, and they investigated the sampling properties of the proposed method.…”

General Quantile Time Series Regressions for Applications in Population Demographics

“…The application of quantile regression models in financial risk and insurance has also recently begun to develop in works such as Dong et al [2015], Peters et al [2016] and discussions in Operational risk contexts in Cruz et al [2015] and . Furthermore, there are Bayesian application works such as Hu et al [2013] which develops a Bayesian partially collapsed Gibbs sampler approach to fitting single-index models in conditional quantile regression. In Bernardi et al [2016b] they consider the challenge of model combining or model averaging in dynamic quantile regression settings which they termed the general dynamic model averaging DMA framework.…”

Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood

“…A Bayesian approach based on the AL likelihood was formally discussed in Yu & Moyeed () for linear quantile regression. In recent years, the AL likelihood has been adopted for Bayesian quantile regression in different contexts and applications, for instance, quantile regression with random effects (Geraci & Bottai, ; Yuan & Yin, ; Geraci & Bottai, ; Yue & Rue, ; Luo et al , ; Wang, ), variable selection for quantile regression (Li et al , ; Alhamzawi et al , ; Alhamzawi & Yu, ; ), spatial quantile regression (Lum & Gelfand, ), quantile regression for count data with application to environmental epidemiology (Lee & Neocleous, ), non‐parametric and semiparametric quantile regression models (Chen & Yu, ; Thompson et al , ; Hu et al , ; Waldmann et al , ; Zhu et al , ; Hu et al , ), quantile regression with fixed censoring (Yu & Stander, ; Kozumi & Kobayashi, ; Kobayashi & Kozumi, ; Yue & Hong, ; Alhamazawi & Yu, ; Zhao & Lian, ), and binary quantile regression (Benoit & Poel, ; Benoit et al , ; Miguéis et al , ).…”