Prediction of Ordered Random Effects in a Simple Small Area Model

TL;DR

This paper investigates the prediction of ordered parameters in small area estimation, demonstrating that shrinkage predictors outperform naive methods and approach the performance of optimal, but often intractable, predictors.

Contribution

It introduces shrinkage-type predictors tailored for ordered parameters in small area models, showing their effectiveness over simple estimates.

Findings

Shrinkage predictors significantly reduce mean squared error.

Naive ordered estimates perform poorly compared to shrinkage methods.

Performance of shrinkage predictors approaches that of optimal predictors.

Abstract

Prediction of a vector of ordered parameters or part of it arises naturally in the context of Small Area Estimation (SAE). For example, one may want to estimate the parameters associated with the top ten areas, the best or worst area, or a certain percentile. We use a simple SAE model to show that estimation of ordered parameters by the corresponding ordered estimates of each area separately does not yield good results with respect to MSE. Shrinkage-type predictors, with an appropriate amount of shrinkage for the particular problem of ordered parameters, are considerably better, and their performance is close to that of the optimal predictors, which cannot in general be computed explicitly.