  We propose a novel methodology relating item response theory methods with
small area estimation strategies in the presence of missing data. Specifically,
we propose an unbiased estimator for the average ability parameter of
three-parameter logistic models. Thus, we carry out an extensive simulation
study in order to compare our estimator with the well-known Horvitz-Thompson
estimator. According to our experiments with synthetic data, our proposal has
substantial lower standard errors than its competitor. In addition, we perform
an actual application by considering the Mathematics results of the 2015
Program for International Student Assessment (PISA), and also, compare our
results with previous analyses. Our findings strongly suggest that our
methodology is a high competitive alternative for generating compelling
official statistics.
