Small-area estimation based on survey data from a left-censored Fay–Herriot model

This paper develops methodology for survey estimation and small-area prediction using Fay–Herriot (1979) models in which the responses are left-censored. Parameter and small-area estimators are derived both by censored-data likelihoods and by an estimating-equation approach which adjusts a Fay–Herriot analysis restricted to the uncensored observations. Formulas for variances of estimators and mean-squared errors of small-area predictions are provided and supported by a simulation study. The methodology is applied to provide diagnostics for the left-censored Fay–Herriot model which are illustrated in the context of the Census Bureauʹs ongoing Small-Area Income and Poverty Estimation (SAIPE) project.