时间：6月8日（周四）上午10:00-11:00
地点：统计楼103
报告题目：Multiple Influential Point Detection in High-Dimensional Spaces
报告人：赵俊龙 北京师范大学统计学院
摘要：
Influence diagnosis should be routinely conducted when one aims to construct a regression model.Despite its importance,the problem of influence quantification is severely under-investigated in a high-dimensional setting,mainly due to the difficulty of establishing a coherent theoretical framework and the lack of easily implementable procedures.Although some progress has been made in recent years, existing approaches are ineffective in detecting multiple influential points especially due to the notorious “masking” and “swamping” effects.To address this challenge,we propose a new group deletion procedure referred to as MIP by introducing two novel quantities named Max and Min statistics.These two statistics 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 pre-specified guarantees.For wider applications, we focus on developing the new proposal for the multiple response regression model,encompassing the univariate response linear model as a special case.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.