部分线性变系数模型的贝叶斯复合分位数回归

doi:10.16088/j.issn.1001-6600.2023102501

Abstract

Abstract: The partial linear variable coefficient model consists of two parts,parameter and non-parameter,which has the advantages of wide range of adaptation and strong interpretation. To solve the parameter estimation problem of the model,the B-spline method is used to approximate the unknown smooth function of the non-parametric part,and then the compound asymmetric Laplacian distribution is used to realize the Bayesian composite quantile regression,and the posterior distribution of all the unknown parameters is derived based on the Gibbs sampling algorithm. Through numerical simulation,Bayesian compound quantile regression is compared with Bayesian quantile regression and Bayesian linear regression parameter estimation. The results show that when the error follows non-normal distribution,Bayesian compound quantile regression estimation performs better under mean square error criterion. Finally,based on the above three methods to predict the case data,the results show that in terms of mean absolute deviation and mean square error prediction,the prediction effect based on Bayesian compound quantile regression is the best.

Key words: partially linear variable coefficient model, B-spline, Bayesian composite quantile regression, mean square error, Gibbs sampling algorithm

CLC Number: O212.1

LI Can, YANG Jianbo, LI Rong. Bayesian Composite Quantile Regression for a Partially Linear Variable Coefficient Model[J].Journal of Guangxi Normal University(Natural Science Edition), 2024, 42(5): 117-129.

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Bayesian Composite Quantile Regression for a Partially Linear Variable Coefficient Model

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