Alternative Mean Square Error Estimators and Confidence Intervals for Prediction of Nonlinear Small Area Parameters

TL;DR

This paper introduces a novel mean square error estimator and calibrated prediction intervals for nonlinear small area parameter prediction, addressing challenges in MSE estimation without full distribution specification.

Contribution

It develops a new MSE estimator that avoids double-bootstrap procedures and constructs less assumption-dependent prediction intervals.

Findings

The proposed MSE estimator performs well in simulations.

Calibration improves the accuracy of prediction intervals.

Methods are successfully applied to agricultural survey data.

Abstract

A difficulty in MSE estimation occurs because we do not specify a full distribution for the survey weights. This obfuscates the use of fully parametric bootstrap procedures. To overcome this challenge, we develop a novel MSE estimator. We estimate the leading term in the MSE, which is the MSE of the best predictor (constructed with the true parameters), using the same simulated samples used to construct the basic predictor. We then exploit the asymptotic normal distribution of the parameter estimators to estimate the second term in the MSE, which reflects variability in the estimated parameters. We incorporate a correction for the bias of the estimator of the leading term without the use of computationally intensive double-bootstrap procedures. We further develop calibrated prediction intervals that rely less on normal theory than standard prediction intervals. We empirically demonstrate the validity of the proposed procedures through extensive simulation studies. We apply the methods to predict several functions of sheet and rill erosion for Iowa counties using data from a complex agricultural survey.