A new robust covariance matrix estimation for high‐dimensional microbiome data

Abstract

SummaryMicrobiome data typically lie in a high‐dimensional simplex. One of the key questions in metagenomic analysis is to exploit the covariance structure for this kind of data. In this paper, a framework called approximate‐estimate‐threshold (AET) is developed for the robust basis covariance estimation for high‐dimensional microbiome data. To be specific, we first construct a proxy matrix , which is almost indistinguishable from the real basis covariance matrix . Then, any estimator satisfying some conditions can be used to estimate . Finally, we impose a thresholding step on to obtain the final estimator . In particular, this paper applies a Huber‐type estimator , and achieves robustness by only requiring the boundedness of 2+ moments for some . We derive the convergence rate of under the spectral norm, and provide theoretical guarantees on support recovery. Extensive simulations and a real example are used to illustrate the empirical performance of our method.