Multiple Influential Point Detection in High-Dimensional Spaces

Influence diagnosis is an integrated component of data analysis, but is severely under-investigated in a high-dimensional setting. One of the key challenges, even in a fixed-dimensional setting, is how to deal with multiple influential points giving rise to the masking and swamping effects. This paper proposes a novel group deletion procedure referred to as MIP by studying two extreme statistics based on a marginal correlation based influence measure. Named the Min and Max statistics, they have complimentary properties in that the Max statistic is effective for overcoming the masking effect while the Min statistic is useful for overcoming the swamping effect. Combining their strengths, we further propose an efficient algorithm that can detect influential points with a prespecified false discovery rate. The proposed influential point detection procedure is simple to implement, efficient to run, and enjoys attractive theoretical properties. Its effectiveness is verified empirically via extensive simulation study and data analysis. An R package implementing the procedure is freely available.