Sparse signal shrinkage and outlier detection in high-dimensional quantile regression with variational Bayes
- Authors
- Lim, Daeyoung; Park, Beomjo; Nott, David; Wang, Xueou; Choi, Taeryon
- Issue Date
- 2020
- Publisher
- INT PRESS BOSTON, INC
- Keywords
- Asymmetric Laplace distribution; Horseshoe plus prior; Outlier detection; Quantile regression; Variational Bayes
- Citation
- STATISTICS AND ITS INTERFACE, v.13, no.2, pp.237 - 249
- Indexed
- SCIE
SCOPUS
- Journal Title
- STATISTICS AND ITS INTERFACE
- Volume
- 13
- Number
- 2
- Start Page
- 237
- End Page
- 249
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/59093
- ISSN
- 1938-7989
- Abstract
- Model misspecification can compromise valid inference in conventional quantile regression models. To address this issue, we consider two flexible model extensions for high-dimensional data. The first is a Bayesian quantile regression approach with variable selection, which uses a sparse signal shrinkage prior on the high-dimensional regression coefficients. The second extension robustifies conventional parametric quantile regression methods by including observation specific mean shift terms. Since the number of outliers is assumed to be small, the vector of mean shifts is sparse, which again motivates the use of a sparse signal shrinkage prior. Specifically, we exploit the horseshoe+ prior distribution for variable selection and outlier detection in the high-dimensional quantile regression models. Computational complexity is alleviated using fast mean field variational Bayes methods, and we compare results obtained by variational methods with those obtained using Markov chain Monte Carlo (MCMC).
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Collections - College of Political Science & Economics > Department of Statistics > 1. Journal Articles
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