  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.
