An adaptive threshold for outlier detection in high-dimensional settings

In this article, we propose a distribution-free method for outlier detection in high-dimensional settings. We employ a series of mirror statistics that can adaptively learn from the dependence structure of the model. We explore the asymptotic properties of these mirror statistics under non Gaussian and mild sparsity assumptions. Subsequently, we derive data-driven thresholds to asymptotically control the false discovery rate (FDR) at various designated levels. Extensive simulations confirm that the proposed method has good FDR control and satisfactory power under the general dependence structure of the model. In addition, an illustrative real case study is presented.