Small Area Estimation with Measurement Error in t Distributed Covariate Variable

Abstract

The large need for small area data and limited auxiliary information drive the development of small area estimation methods with auxiliary information comes from survey data. The consequence of the existence of the auxiliary variables from survey data is the development of measurement error models. Survey data is used as auxiliary variables that are taken randomly so that the data is considered to be stochastic. Thus, the measurement error model is assumed to be structural. Meanwhile, auxiliary information or covariates does not always have a normal distribution but sometimes contain outliers so the assumption of the t-distribution is considered to be more appropriate. Therefore, we use the moment-method to estimate the parameters and develop an empirical Bayes-EB predictor in a nested error regression model with measurement errors in the area-level covariates. In addition, the covariate in this model is assumed in the t-distribution which were previously always considered normal. Using simulation studies, we can report the performance of EB predictor under true covariates and measurement errors assumed to be t-distributions based on mean squared prediction errors (EMSPE). The results show that the model we developed leads to a significant increase in efficiency compared to EB predictors previously proposed. Furthermore, this approach is applied in National socio-economic survey (Susenas) data in Malang Regency with the aim of predicting mean years of schooling by districts using monthly per capita household expenditure data as the covariate variables that are considered to have the t-distribution.