Journal of Data Science

In semiparametric regression it is of interest to detect anomalous observations that exert an unduly large influence on the parameter’s esti-mate and fitted values. Usually the existence of influential observations is complicated by the presence of collinearity. However no method of influ-ence diagnostics available for the possible effects that collinearity can have on the influence of an observation on the estimates of parametric and non-parametric component of semiparametric regression models. In this paper we show when Liu estimators are used to mitigate the effects of collinearity the influence of some observations can be drastically modified. We propose a case deletion formula to detect influential points in Liu estimators of semi-parametric regression models . As an illustrative example a real data set are analysed.