Two-layer EM algorithm for ALD mixture regression models: A new solution to composite quantile regression

Shangshan Wang and Liming Xiang

Computational Statistics & Data Analysis, 2017, vol. 115, issue C, 136-154

Abstract: We advocate linear regression by modeling the error term through a finite mixture of asymmetric Laplace distributions (ALDs). The model expands the flexibility of linear regression to account for heterogeneity among data and allows us to establish the equivalence between maximum likelihood estimation of the model parameters and the composite quantile regression (CQR) estimation developed by Zou and Yuan (Ann. Stat. 36:1108–1126, 2008), providing a new likelihood-based solution to CQR. Particularly, we develop a computationally efficient estimation procedure via a two-layer EM algorithm, where the first layer EM algorithm incorporates missing information from the component memberships of the mixture model and nests the second layer EM in its M-step to accommodate latent variables involved in the location-scale mixture representation of the ALD. An appealing feature of the proposed algorithm is that the closed form updates for parameters in each iteration are obtained explicitly, instead of resorting to numerical optimization methods as in the existing work. Computational complexity can be reduced significantly. We evaluate the performance through simulation studies and illustrate its usefulness by analyzing a gene expression dataset.

Keywords: Asymmetric Laplace distribution; Composite quantile regression; EM algorithm; Mixture regression model; Robustness (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S016794731730141X
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:115:y:2017:i:c:p:136-154

DOI: 10.1016/j.csda.2017.06.002

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().