Ávila Valdez, José Luis, <br/><br/>
Usingthe EM algorithm in small area estimation whith the Fay-Herriot model / 
José Luis Ávila Valdez. 
 - 123 hojas. 
<br/><br/> CONICYT - PCHA/Doctorado Nacional/2014-63140019. 
<br/><br/>Doctorado en Estadística. 
<br/><br/> Standard methods of variance component estimation used in the Fay-Herriot model for small area estimation can produce inadmissible (negative or zero) values of these variances. This implies that the empirical best linear unbiased predictor of a small area mean does not take into account the variance of the random effect of small areas, reducing it only to a regression estimator. In this work, we consider an approach based on the expectation-maximization (EM) algorithm to solve this problem of inadmissibility in both univariate and multivariate Fay-Herriot model. We show through Monte Carlo simulations that the EM algorithm always produces strictly positive model variance component estimates. In the univariate case, we compare the performance of the proposed approach for two recent methods in terms of relative bias, mean square error and mean square predictor error. We apply our approach to a food security and poverty data set collected in Mexico. 
<br/><br/><label>Subjects--Topical Terms: </label><br/>ALGORITMOS.<br/>ALGORITMOS DE EXPECTACION - MAXIMIZACION.<br/>MAXIMOS Y MINIMOS.