  Partially linear additive models generalize linear ones since they model the
relation between a response variable and covariates by assuming that some
covariates have a linear relation with the response but each of the others
enter through unknown univariate smooth functions. The harmful effect of
outliers either in the residuals or in the covariates involved in the linear
component has been described in the situation of partially linear models, that
is, when only one nonparametric component is involved in the model. When
dealing with additive components, the problem of providing reliable estimators
when atypical data arise, is of practical importance motivating the need of
robust procedures. Hence, we propose a family of robust estimators for
partially linear additive models by combining $B-$splines with robust linear
regression estimators. We obtain consistency results, rates of convergence and
asymptotic normality for the linear components, under mild assumptions. A Monte
Carlo study is carried out to compare the performance of the robust proposal
with its classical counterpart under different models and contamination
schemes. The numerical experiments show the advantage of the proposed
methodology for finite samples. We also illustrate the usefulness of the
proposed approach on a real data set.
