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Screening and Clustering of Sparse Regressions with Finite Non-Gaussian Mixtures

Zhang, Jian (2016) Screening and Clustering of Sparse Regressions with Finite Non-Gaussian Mixtures. Biometrics, 73 (2). pp. 540-550. ISSN 0006-341X. (doi:10.1111/biom.12585)

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This article proposes a method to address the problem that can arise when covariates in a regression setting are not Gaussian, which may give rise to approximately mixture-distributed errors, or when a true mixture of regressions produced the data. The method begins with non- Gaussian mixture-based marginal variable screening, followed by fitting a full but relatively smaller mixture regression model to the selected data with help of a new penalization scheme. Under certain regularity conditions, the new screening procedure is shown to possess a sure screening property even when the population is heterogeneous. We further prove that there exists an elbow-point in the associated scree plot which results in a consistent estimator of the set of active covariates in the model. By simulations, we demonstrate that the new procedure can substantially improve the performance of the existing procedures in the content of variable screening and data clustering. By applying the proposed procedure to motif data analysis in molecular biology, we demonstrate that the new method holds promise in practice.

Item Type: Article
DOI/Identification number: 10.1111/biom.12585
Projects: [UNSPECIFIED] High dimensional inferences with applications
Uncontrolled keywords: Heterogeneity, non-Gaussian mixture regression models, component-wise regularization, simultaneous clustering and variable screening.
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Jian Zhang
Date Deposited: 05 Sep 2016 16:21 UTC
Last Modified: 29 May 2019 17:47 UTC
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