Abstract: A general framework for a local influence analysis is developed for sufficient dimension reduction when the data likelihood is absent and the inference result is a space rather than a vector. A clear and intuitive interpretation of this approach is described. Its application to the sliced inverse regression is presented, together with its invariance properties. A data trimming strategy is also suggested, based on the influence assessment for observations provided by our method. A simulation study and a real-data analysis are presented. The results indicate that the local influence analysis avoids the masking effect, and that the data trimming provides a substantial increase in the inference accuracy.

Keywords: Central subspace, displacement function, influence measure, perturbation scheme.