Trimming influential observations for improved single-index model estimated sufficient summary plots

The detection and subsequent treatment of influential observations have been well covered with respect to ordinary least squares (OLS) under an assumed multiple linear regression (MLR) model using measures such as Cook's Distance. However, OLS can be shown to be a useful method under a much wider variety of models. The purpose of this paper is twofold. Firstly we introduce a new diagnostic, similar to Cook's Distance, that is useful for detecting influential observations under an assumed single-index model. Secondly we show, via simulation, how trimming observations according to such diagnostics can greatly benefit the analysis even when no gross outliers are evident.