In this article, we describe and apply the Fay-Herriot model with spatially correlated random area effects (Pratesi & Salvati, 2006) in order to predict the prevalence of anemia and childhood stunting in Peruvian districts. This prediction is based on data from the Demographic and Family Health Survey of the year 2019, which collects information about anemia and childhood stunting in children under the age of 12 years, as well as the National Census carried out in 2017. Our main objective is to produce reliable predictions for districts with sample sizes too small to provide accurate direct estimates, as well as for districts not included in the sample. The basic Fay-Herriot model (Fay & Herriot, 1979) addresses this issue by incorporating auxiliary information, typically available from administrative or census records. The Fay-Herriot model with spatially correlated random area ...