Estimation and Statistical Inference for Partial Correlations

• Activity Number: 509
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Tingni Sun*+ and Cun-Hui Zhang
• Companies: Rutgers University and Rutgers University
• Keywords: asymptotic normality ; estimation ; inference ; Lasso ; partial correlation

Abstract

Most of the recent advances in high-dimensional data have been focused on the estimation of high-dimensional objects. However, the estimation of low-dimensional functionals of high-dimensional parameters is also of great interest. We consider efficient estimation of partial correlation between individual pairs of variables with high-dimensional Gaussian data. Our procedure is based on scaled Lasso, a joint estimator for the regression coefficient and noise level. We develop asymptotic normality of the proposed estimator under certain "large-p-smaller-n" setting, which directly leads to statistical inference about partial correlation. The condition here is weaker than that in the existing results based on variable selection.