Detection of influential observations in semiparametric regression model

In this article, we consider the semiparametric regression model and examine influential observations which have undue effects on the estimators for this model. One of the approaches to measure the influence of an individual observation is to delete the observation from the data. The most common measure based on this approach is Cook's distance. Recently, Daniel Peña introduced a new measure based on this approach. Pena's measure is able to detect high leverage outliers, which could be undetected by Cook's distance, in large data sets in linear regression model. The Cook's distances for parameter vector, unknown smooth function and response variable in semiparametric regression model are expressed by authors as functions of the residuals and leverages. Following the study of them we derive a type of Pena's measure as functions of the residuals and leverages for the same model. We compare the performance of these measures as to detection of influential observations using real data, artificial data and simulation. The results show that the performance of Pena's measure is better than Cook's distance to detect high leverage outliers in large data sets in the semiparametric regression model such as in the linear regression model.