New Bootstrap Bias Corrections with Application to Estimation of Prediction MSE in Small Area Estimation
Solange Correa
Department of Methods and Quality, Brazilian Institute of Geography and Statistics, Rio de Janeiro, Brazil

In this paper, a new method for bias correction is proposed. The approach models the error of the target estimator as a function of the corresponding bootstrap estimator, and the original estimators and bootstrap estimators when estimating the parameters governing the model underlying the sample data. This is achieved by considering a large set of plausible parameter values, generating pseudo original samples and bootstrap samples for each parameter and then searching for an appropriate functional relationship. Under certain conditions, the use of this procedure permits also estimating the MSE of the bias corrected estimators. The method is applied for estimating the prediction MSE in small area estimation of proportions under a logistic mixed model. Empirical comparisons with the Jackknife and classical bootstrap procedures based on a simulation study are presented.

Keywords: Best predictor; Empirical best predictor; Logistic mixed models; Jackknife

Biography: Dr. Solange Correa has been methodologist at the Brazilian Institute of Geography and Statistics for 14 years. She finished her Ph.D. on “Bias corrections in multilevel modelling of survey data with applications to small area estimation” in 2008 at the University of Southampton, U.K., under joint supervision of Professor Danny Pfeffermann and Professor Chris Skinner.