Abstract
In this Note, we introduce the local linear estimation of the conditional density of a scalar response variable given a random variable taking values in a semi-metric space. Under some general conditions, we establish the pointwise and uniform almost complete convergences with rates of this estimator. Moreover, as an application, we use the obtained results to derive some asymptotic properties for the local linear estimator of the conditional mode. (C) 2010 Academie des sciences. Publie par Elsevier Masson SAS.