Estimating Large Correlation Matrices by Banding the Partial Autocorrelation Matrix

• Activity Number: 672
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yanpin Wang*+ and Michael Daniels
• Companies: University of Florida and University of Florida
• Keywords: Partial Autocorrelation Matrix ; k-Band Matrix ; Hypothesis Testing ; Bonferroni Correction

Abstract

In this article, we propose a computationally efficient approach to estimate (large) p-dimensional correlation matrices of ordered data based on an independent sample of size $n$. To do this, we construct the estimator based on a k-band partial autocorrelation matrix with the number of bands chosen using an exact multiple hypothesis testing procedure. This approach is considerably faster than many existing methods and only requires inversion of $k$ dimensional covariances matrices. In addition, the resulting estimator is guaranteed to be positive definite as long as $k \leq n-2$ (even when $n < p$). We evaluate our estimator via extensive simulations and compare it to the Ledoit-Wolf estimator. We also illustrate the approach using high-dimensional sonar data.