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Bayesian analysis of quantile principal component regression model
Journal of the Korean Data & Information Science Society 2021;32:739-55
Published online July 31, 2021;  https://doi.org/10.7465/jkdi.2021.32.4.739
© 2021 Korean Data and Information Science Society.

Minjung Kyung1

1Department of Statistics, Duksung Women’s University
Correspondence to: This work was supported by the Duksung Women’s University research grants 3000005247.
1 Associate professor, Department of Statistics, Duksung Women’s University, Seoul 132-714, Korea.
E-mail: mkyung@duksung.ac.kr
Received April 5, 2021; Revised June 2, 2021; Accepted June 2, 2021.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Quantile regression model has been known as a strong tool even for non-normal and non-homoscedasticity response. Principal component analysis (PCA) which has been considered as a method for dimension reduction is a useful tool when there exists a multicollinearity problem among explanatory variables. We suggest a Bayesian inference for quantile PCA regression with subset of principal components based on singular value decomposition, and we consider shrinkage priors on selected components with large variance. We choose the number of components considering the linear relationship with dependent variable based on the Bayesian information criteria and we use the least-norm inverse for the inference of original quantile regression parameters. Applications to real datasets are discussed.
Keywords : Bayesian inference, Bayesian information criteria, principal component regression, quantile regression, singular value decomposition.