Local influence analysis for the sliced average third‐moment estimation

Sliced average third‐moment estimation (SATME) is a typical method for sufficient dimension reduction (SDR) based on high‐order conditional moment. It is useful, particularly in the scenarios of regression mixtures. However, as SATME uses the third‐order conditional moment of the predictors given the response, it may not as robust as some other SDR methods that use lower order moments, say, sliced inverse regression (SIR) and slice average variance estimation (SAVE). Based on the space displacement function, a local influence analysis framework of SATME is constructed including a statistic of influence assessment for the observations. Furthermore, a data‐trimming strategy is suggested based on the above influence assessment. The proposed methodologies solve a typical issue that also exists in some other SDR methods. A real‐data analysis and simulations are presented.