Influential Observations Detection by Random Projection in High-Dimensional Multivariate Response Linear Model

In this article, we consider the challenging problem of influential point detection in high-dimensional linear regressions with multivariate responses. A Multivariate Response Influential Point (MRIP) detection algorithm is proposed based on a novel random projection method, which takes into account the dependence among the responses. When the number of projected directions tends to infinity, the limit statistic is derived, which simplifies the computations greatly. The proposed MRIP algorithm can mitigate the adverse effects of masking and swamping effectively. The experimental results on both simulated and real datasets demonstrate that the proposed method outperforms existing state-of-the-art methods. The proposed method is computationally efficient and scalable to large datasets, making it practical for real-world applications. Supplementary materials for this article are available online.