Local influence for Student-t partially linear models

In this paper we extend partial linear models with normal errors to Student-t errors. Penalized likelihood equations are applied to derive the maximum likelihood estimates which appear to be robust against outlying observations in the sense of the Mahalanobis distance. In order to study the sensitivity of the penalized estimates under some usual perturbation schemes in the model or data, the local influence curvatures are derived and some diagnostic graphics are proposed. A motivating example preliminary analyzed under normal errors is reanalyzed under Student-t errors. The local influence approach is used to compare the sensitivity of the model estimates.