  In this paper we attempt to answer the following question: ``Is it possible
to obtain reliable estimates for the prevalence of anemia rates in children
under five years in the districts of Peru?'' Specifically, the interest of the
present paper is to understand to which extent employing the basic and the
spatial Fay-Herriot models can compensate for inadequate sample size in most of
the sampled districts, and whether the way of choosing the spatial neighbors
has an impact on the resulting inference. Furthermore, it is raised the
question of how to choose an optimal way to define the neighbours. We present
an illustrative analysis using the data from the Demographic and Family Health
Survey of the year 2019, and the National Census carried out in 2017.
