High-dimensional Covariance Estimation by Pairwise Likelihood Truncation

• DOI: 10.48550/arxiv.2407.07717
• Publication Date: 2024-07-10
• Authors: Alessandro Casa; Davide Ferrari; Zhendong Huang
• Keywords: Truncation (statistics)

Pairwise likelihood offers a useful approximation to the full function for covariance estimation in high-dimensional context. It simplifies dependencies by combining marginal bivariate objects, thereby making more manageable. In certain models, including Gaussian model, both pairwise and likelihoods are known be maximized same parameter values, thus retaining optimal statistical efficiency, when number of variables is fixed. Leveraging this insight, we introduce sparse matrices maximizing truncated version function, which focuses on terms corresponding nonzero elements. To achieve meaningful truncation, propose minimize discrepancy between scores plus an L1-penalty discouraging inclusion uninformative terms. Differently from other regularization approaches, our method selects whole objects rather than individual parameters, inherent unbiasedness estimating equations. This selection procedure shown have consistency property as dimension increases exponentially fast. As result, implied estimator consistent converges oracle maximum that assumes knowledge entries.