Bayesian composite $$L^p$$ -quantile regression

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Metrika Pub Date : 2024-02-21 DOI:10.1007/s00184-024-00950-8

引用次数: 0

Abstract

$L^p$ -quantiles are a class of generalized quantiles defined as minimizers of an asymmetric power function. They include both quantiles, $p=1$ , and expectiles, $p=2$ , as special cases. This paper studies composite $L^p$ -quantile regression, simultaneously extending single $L^p$ -quantile regression and composite quantile regression. A Bayesian approach is considered, where a novel parameterization of the skewed exponential power distribution is utilized. Further, a Laplace prior on the regression coefficients allows for variable selection. Through a Monte Carlo study and applications to empirical data, the proposed method is shown to outperform Bayesian composite quantile regression in most aspects.

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贝叶斯综合 $$L^p$$ -quantile 回归

Abstract $L^p$ -quantiles 是一类定义为非对称幂函数最小化的广义量值。它们包括量值（p=1）和期望值（p=2）作为特例。本文研究了复合量值回归，同时扩展了单一量值回归和复合量值回归。研究考虑了一种贝叶斯方法，利用了倾斜指数幂分布的新参数化。此外，回归系数的拉普拉斯先验允许进行变量选择。通过蒙特卡罗研究和对经验数据的应用，证明所提出的方法在大多数方面优于贝叶斯复合量化回归。

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

Metrika 数学-统计学与概率论

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Metrika is an international journal for theoretical and applied statistics. Metrika publishes original research papers in the field of mathematical statistics and statistical methods. Great importance is attached to new developments in theoretical statistics, statistical modeling and to actual innovative applicability of the proposed statistical methods and results. Topics of interest include, without being limited to, multivariate analysis, high dimensional statistics and nonparametric statistics; categorical data analysis and latent variable models; reliability, lifetime data analysis and statistics in engineering sciences.