Simultaneous Prediction Intervals for Small Area Parameter
share
In this paper we address the construction of simultaneous prediction intervals for small area parameters in linear mixed models. Simultaneous intervals are necessary to compare areas, or to look at several areas at a time, as the presently available intervals are not statistically valid for these scenarios. We consider two frameworks to develop simultaneous intervals: the Monte Carlo approximation of the volume of a tube based intervals and bootstrap bands. Proofs of the consistency as well as the asymptotic coverage probability of the bootstrap intervals are provided. Our proposal is accompanied by simulation experiments and a data example. The simulations show which method works best under a particular scenario. We illustrate the utility of simultaneous intervals for the analysis of small area parameters. When comparing the areas, the classical methods lead to erroneous conclusions, visible in the study of the household income distribution in Galicia in Northern Spain.
READ FULL TEXT