Estimation of Linear and Non-Linear Indicators using Interval Censored Income Data

Abstract

Among a variety of small area estimation methods, one popular approach for the estimation of linear and non-linear indicators is the empirical best predictor. However, parameter estimation using standard maximum likelihood methods is not possible, when the dependent variable of the underlying nested error regression model, is censored to specific intervals. This is often the case for income variables. Therefore, this work proposes an estimation method, which enables the estimation of the regression parameters of the nested error regression model using interval censored data. The introduced method is based on the stochastic expectation maximization algorithm. Since the stochastic expectation maximization method relies on the Gaussian assumptions of the error terms, transformations are incorporated into the algorithm to handle departures from normality. The estimation of the mean squared error of the empirical best predictors is facilitated by a parametric bootstrap which captures the additional uncertainty coming from the interval censored dependent variable. The validity of the proposed method is validated by extensive model-based simulations.