Flexible Bayesian quantile regression based on the generalized asymmetric Huberised-type distribution

IF 1.6 2区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Statistics and Computing Pub Date : 2024-06-27 DOI:10.1007/s11222-024-10453-1

Weitao Hu, Weiping Zhang

引用次数: 0

Abstract

To enhance the robustness and flexibility of Bayesian quantile regression models using the asymmetric Laplace or asymmetric Huberised-type (AH) distribution, which lacks changeable mode, diminishing influence of outliers, and asymmetry under median regression, we propose a new generalized AH distribution which is achieved through a hierarchical mixture representation, thus leading to a flexible Bayesian Huberised quantile regression framework. With many parameters in the model, we develop an efficient Markov chain Monte Carlo procedure based on the Metropolis-within-Gibbs sampling algorithm. The robustness and flexibility of the new distribution are examined through intensive simulation studies and application to two real data sets.

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基于广义非对称胡贝利兹型分布的灵活贝叶斯量化回归

非对称拉普拉斯或非对称休伯里化型（AH）分布缺乏可变模式、离群值影响减弱和中位回归下的非对称性，为了增强使用该分布的贝叶斯量化回归模型的稳健性和灵活性，我们提出了一种新的广义 AH 分布，该分布通过分层混合表示来实现，从而产生了一种灵活的贝叶斯休伯里化量化回归框架。由于模型中有许多参数，我们基于 Metropolis-within-Gibbs 采样算法开发了一种高效的马尔可夫链蒙特卡罗程序。通过深入的模拟研究和对两个真实数据集的应用，检验了新分布的稳健性和灵活性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics and Computing 数学-计算机：理论方法

CiteScore

3.20

自引率

4.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Statistics and Computing is a bi-monthly refereed journal which publishes papers covering the range of the interface between the statistical and computing sciences. In particular, it addresses the use of statistical concepts in computing science, for example in machine learning, computer vision and data analytics, as well as the use of computers in data modelling, prediction and analysis. Specific topics which are covered include: techniques for evaluating analytically intractable problems such as bootstrap resampling, Markov chain Monte Carlo, sequential Monte Carlo, approximate Bayesian computation, search and optimization methods, stochastic simulation and Monte Carlo, graphics, computer environments, statistical approaches to software errors, information retrieval, machine learning, statistics of databases and database technology, huge data sets and big data analytics, computer algebra, graphical models, image processing, tomography, inverse problems and uncertainty quantification. In addition, the journal contains original research reports, authoritative review papers, discussed papers, and occasional special issues on particular topics or carrying proceedings of relevant conferences. Statistics and Computing also publishes book review and software review sections.