Bootstrap Mean Squared Error of a Small-Area EBLUP Articles uri icon

publication date

  • May 2008

start page

  • 443

end page

  • 462

issue

  • 5

volume

  • 78

international standard serial number (ISSN)

  • 0094-9655

electronic international standard serial number (EISSN)

  • 1563-5163

abstract

  • Concerning the estimation of linear parameters in small areas, a nested-error regression model is assumed for the values of the target variable in the units of a finite population. Then, a bootstrap procedure is proposed for estimating the mean squared error (MSE) of the EBLUP under the finite population setup. The consistency of the bootstrap procedure is studied, and a simulation experiment is carried out in order to compare the performance of two different bootstrap estimators with the approximation given by Prasad and Rao [Prasad, N.G.N. and Rao, J.N.K., 1990, The estimation of the mean squared error of small-area estimators. Journal of the American Statistical Association, 85, 163&-171.]. In the numerical results, one of the bootstrap estimators shows a better bias behavior thanthe Prasad&-Rao approximation for some of the small areas and not much worse in any case. Further, it shows less MSE in situations of moderate heteroscedasticity and under mispecification of the error distribution as normal when the true distribution is logistic or Gumbel. The proposed bootstrap method can be applied to more general types of parameters (linear of not) and predictors.