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Flexible Bayesian quantile curve fitting with shape restrictions under the Dirichlet process mixture of the generalized asymmetric Laplace distribution

Authors
Kobayashi, GenyaRoh, TaeyoungLee, JangwonChoi, Taeryon
Issue Date
2021
Publisher
WILEY
Keywords
Bayesian nonlinear quantile regression; censored data; Gaussian process; generalized asymmetric Laplace distribution; shape restriction
Citation
CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE, v.49, no.3, pp.698 - 730
Indexed
SCIE
SCOPUS
Journal Title
CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE
Volume
49
Number
3
Start Page
698
End Page
730
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/144860
DOI
10.1002/cjs.11582
ISSN
0319-5724
Abstract
We propose a flexible Bayesian semiparametric quantile regression model based on Dirichlet process mixtures of generalized asymmetric Laplace distributions for fitting curves with shape restrictions. The generalized asymmetric Laplace distribution exhibits more flexible tail behaviour than the frequently used asymmetric Laplace distribution in Bayesian quantile regression. In addition, nonparametric mixing over the shape and scale parameters with the Dirichlet process mixture extends its flexibility and improves the goodness of fit. By assuming the derivatives of the regression functions to be the squares of the Gaussian processes, our approach ensures that the resulting functions have shape restrictions such as monotonicity, convexity and concavity. The introduction of shape restrictions prevents overfitting and helps obtain smoother and more stable estimates of the quantile curves, especially in the tail quantiles for small and moderate sample sizes. Furthermore, the proposed shape-restricted quantile semiparametric regression model deals with sparse estimation for regression coefficients using the horseshoe+ prior distribution, and it is extended to cases with group-specific curve estimation and censored data. The usefulness of the proposed models is demonstrated using simulated datasets and real applications.
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정경대학 (통계학과)
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