# Detecting influential observations on the sliced inverse regression dimension reduction subspace

*by Dr Luke Prendergast*

*Institution:*La Trobe University

*Date: Thu 3rd November 2005*

*Time: 2:00 PM*

*Location: Theatre 2, Old Geology Building, University of Melbourne*

*Abstract*: Sliced Inverse Regression is a useful dimension reduction technique that may be employed as a pre-step to model fitting in regression analysis. Under some mild conditions SIR seeks a small number of linear combinations of the predictor variables that contains all of the required regression information without knowledge of the exact structural relationship between the response and predictors. The directions that define these linear combinations are known as effective dimension reduction (e.d.r.) directions and the space spanned by them is known as the e.d.r. space. Due to the non-uniqueness of these e.d.r. directions it is the goal of SIR to estimate a basis for the e.d.r. space.

There has been much work on the development of influence measures for the detection of influential observations with respect to methods such as least squares regression. However, there is a lack of influence measures for recently developed methods such as SIR in part due to the fact that only a general regression model is assumed. In this talk I will demonstrate how the influence function may be used to highlight which types of observations have high influence on the estimation of the e.d.r. space which may be otherwise difficult to detect. I will then use sample versions of the influence function, applied to both real and simulated data sets, to highlight the usefulness of this approach in practice.

*For More Information:* Owen Jones tel. 8344-6412 email: o.jones@ms.unimelb.edu.au