Title: Small area estimation: A nonparametric maximum likelihood approach
Authors: Maria Francesca Marino - University of Perugia (Italy) [presenting]
Maria Giovanna Ranalli - University of Perugia (Italy)
Nicola Salvati - University of Pisa (Italy)
Marco Alfo - University La Sapienza, Rome (Italy)
Abstract: When dealing with small area estimation, generalized linear mixed models represent a typical frequentist tool for deriving best prediction of counts or proportions. Area-specific Gaussian random parameters are typically considered to account for sources of unobserved heterogeneity that are not captured by the covariates in the model. However, for non-Gaussian responses, computing the EBP and the corresponding MSE requires the solution of (possibly) multiple integrals that do not admit closed form. Monte Carlo methods and parametric bootstrap are frequent choices even if the computational burden represents a non trivial task. We propose to estimate model parameters via a nonparametric maximum likelihood approach (NPML). We derive the EBP and the analytic approximation to its MSE. NPML allows us to avoid unverifiable assumptions on the random parameter distribution: as long as the likelihood is bounded, its maximization leads to a finite mixture distribution with at most as many support points as the number of distinct area profiles. Also, since mixture parameters are directly estimated from the data, extreme and/or asymmetric departures from the homogeneous model can be accommodated. Last, given the discrete nature of the mixing distribution, we can avoid integrals approximation and Monte Carlo integration thus considerably reducing the computational effort.