Parametric bootstrap mean squared error of a small area multivariate EBLUP

Abstract

This article deals with mean squared error (MSE) estimation of a multivariate empirical best linear unbiased predictor (MEBLUP) under the unit-level multivariate nested-errors regression model for small area estimation via parametric bootstrap. A simulation study is designed to evaluate the performance of our algorithm and compare it with the univariate case bootstrap MSE which has been shown to be consistent to the true MSE. The simulation shows that, in line with the literature, MEBLUP provides unbiased estimates with lower MSE than EBLUP. We also provide a short empirical analysis based on real data collected from the U.S. Department of Agriculture.

Keywords:

• Multivariate empirical best Linear unbiased predictor
• Model-based inference
• Multivariate small area estimation
• Multivariate Multilevel models
• Resampling

Additional information

Funding

This research was financially supported by the UK Economic and Social Research Council (ESRC), grant number ES/J500094/1.