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Multitask Quantile Regression under the Transnormal Model.

ABSTRACT: We consider estimating multi-task quantile regression under the transnormal model, with focus on high-dimensional setting. We derive a surprisingly simple closed-form solution through rank-based covariance regularization. In particular, we propose the rank-based ?1 penalization with positive definite constraints for estimating sparse covariance matrices, and the rank-based banded Cholesky decomposition regularization for estimating banded precision matrices. By taking advantage of alternating direction method of multipliers, nearest correlation matrix projection is introduced that inherits sampling properties of the unprojected one. Our work combines strengths of quantile regression and rank-based covariance regularization to simultaneously deal with nonlinearity and nonnormality for high-dimensional regression. Furthermore, the proposed method strikes a good balance between robustness and efficiency, achieves the "oracle"-like convergence rate, and provides the provable prediction interval under the high-dimensional setting. The finite-sample performance of the proposed method is also examined. The performance of our proposed rank-based method is demonstrated in a real application to analyze the protein mass spectroscopy data.

SUBMITTER: Fan J

PROVIDER: S-EPMC5662245 | biostudies-literature | 2016

REPOSITORIES: biostudies-literature

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Publications

Multitask Quantile Regression under the Transnormal Model.

Fan Jianqing J Xue Lingzhou L Zou Hui H

Journal of the American Statistical Association 20160101 516

We consider estimating multi-task quantile regression under the transnormal model, with focus on high-dimensional setting. We derive a surprisingly simple closed-form solution through rank-based covariance regularization. In particular, we propose the rank-based <i>ℓ</i><sub>1</sub> penalization with positive definite constraints for estimating sparse covariance matrices, and the rank-based banded Cholesky decomposition regularization for estimating banded precision matrices. By taking advantage ...[more]

PMID: 29097827

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Project description:BACKGROUND:Under-five malnutrition is a major public health issue contributing to mortality and morbidity, especially in developing countries like Ghana where the rates remain unacceptably high. Identification of critical risk factors of under-five malnutrition using appropriate and advanced statistical methods can help formulate appropriate health programmes and policies aimed at achieving the United Nations SDG Goal 2 target 2. This study attempts to develop a simultaneous quantile regression, an in-depth statistical model to identify critical risk factors of under-five severe chronic malnutrition (severe stunting). METHODS:Based on the nationally representative data from the 2014 Ghana Demographic and Health Survey, height-for-age z-score (HAZ) was estimated. Multivariable simultaneous quantile regression modelling was employed to identify critical risk factors for severe stunting based on HAZ (a measure of chronic malnutrition in populations). Quantiles of HAZ with focus on severe stunting were modelled and the impact of the risk factors determined. Significant test of the difference between slopes at different selected quantiles of severe stunting and other quantiles were performed. A quantile regression plots of slopes were developed to visually examine the impact of the risk factors across these quantiles. RESULTS:Data on a total of 2716 children were analysed out of which 144 (5.3%) were severely stunted. The models identified child level factors such as type of birth, sex, age, place of delivery and size at birth as significant risk factors of under-five severe stunting. Maternal and household level factors identified as significant predictors of under-five severe stunting were maternal age and education, maternal national health insurance status, household wealth status, and number of children under-five in households. Highly significant differences exist in the slopes between 0.1 and 0.9 quantiles. The quantile regression plots for the selected quantiles from 0.1 to 0.9 showed substantial differences in the impact of the covariates across the quantiles of HAZ considered. CONCLUSION:Critical risk factors that can aid formulation of child nutrition and health policies and interventions that will improve child nutritional outcomes and survival were identified. Modelling under-five severe stunting using multivariable simultaneous quantile regression models could be beneficial to addressing the under-five severe stunting.

Dataset Information

Multitask Quantile Regression under the Transnormal Model.

Publications

Multitask Quantile Regression under the Transnormal Model.

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