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Covariate-Adjusted Precision Matrix Estimation with an Application in Genetical Genomics.

Publication ,  Journal Article
Cai, TT; Li, H; Liu, W; Xie, J
Published in: Biometrika
March 2013

Motivated by analysis of genetical genomics data, we introduce a sparse high dimensional multivariate regression model for studying conditional independence relationships among a set of genes adjusting for possible genetic effects. The precision matrix in the model specifies a covariate-adjusted Gaussian graph, which presents the conditional dependence structure of gene expression after the confounding genetic effects on gene expression are taken into account. We present a covariate-adjusted precision matrix estimation method using a constrained ℓ1 minimization, which can be easily implemented by linear programming. Asymptotic convergence rates in various matrix norms and sign consistency are established for the estimators of the regression coefficients and the precision matrix, allowing both the number of genes and the number of the genetic variants to diverge. Simulation shows that the proposed method results in significant improvements in both precision matrix estimation and graphical structure selection when compared to the standard Gaussian graphical model assuming constant means. The proposed method is also applied to analyze a yeast genetical genomics data for the identification of the gene network among a set of genes in the mitogen-activated protein kinase pathway.

Duke Scholars

Published In

Biometrika

DOI

ISSN

0006-3444

Publication Date

March 2013

Volume

100

Issue

1

Start / End Page

139 / 156

Location

England

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics
 

Citation

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ICMJE
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Cai, T. T., Li, H., Liu, W., & Xie, J. (2013). Covariate-Adjusted Precision Matrix Estimation with an Application in Genetical Genomics. Biometrika, 100(1), 139–156. https://doi.org/10.1093/biomet/ass058
Cai, T Tony, Hongzhe Li, Weidong Liu, and Jichun Xie. “Covariate-Adjusted Precision Matrix Estimation with an Application in Genetical Genomics.Biometrika 100, no. 1 (March 2013): 139–56. https://doi.org/10.1093/biomet/ass058.
Cai TT, Li H, Liu W, Xie J. Covariate-Adjusted Precision Matrix Estimation with an Application in Genetical Genomics. Biometrika. 2013 Mar;100(1):139–56.
Cai, T. Tony, et al. “Covariate-Adjusted Precision Matrix Estimation with an Application in Genetical Genomics.Biometrika, vol. 100, no. 1, Mar. 2013, pp. 139–56. Pubmed, doi:10.1093/biomet/ass058.
Cai TT, Li H, Liu W, Xie J. Covariate-Adjusted Precision Matrix Estimation with an Application in Genetical Genomics. Biometrika. 2013 Mar;100(1):139–156.
Journal cover image

Published In

Biometrika

DOI

ISSN

0006-3444

Publication Date

March 2013

Volume

100

Issue

1

Start / End Page

139 / 156

Location

England

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics