Estimation for Basis Precision Matrix by Unconstrained l1‐Regularized Estimator

Basis precision matrix plays fundamental roles in the study of compositional data. Constrained and unconstrained optimization methods are usually used to estimate basis precision matrices. Zhang and He (2019) discuss that problem by an unconstrained optimization estimator. However, the authors do not give any convergence rates. Zhang et al. (2025) define their constrained optimization estimator and provide a convergence rate. In this paper, we extend Zhang and He's work. It turns out that our unconstrained ‐regularized estimator attains the same convergence rate as the one of Zhang et al. Moreover, our estimator outperforms Zhang et al.'s for numerical experiments.