Sparse basis covariance matrix estimation for high dimensional compositional data via hard thresholding

Abstract

Motivated by the high-dimensional compositional data appearing in many fields, this paper addresses the problem of large covariance estimation for compositional data. Firstly, we introduce the hard thresholding estimator to approximate the sparse basis covariance matrix which is relevant with compositional data. Then the upper error bounds are measured by the general matrix lv,w-norm and the general entrywise Lv,w-norm respectively with v,w∈[1,∞] in terms of probability. Finally, numerical simulations and real datasets application demonstrate that our estimator is close to the oracle estimator and outperforms the COAT estimator proposed by Cao et al. (2019).