Small area estimation for autoregressive model with measurement error in the auxiliary variable

Abstract

Small Area Estimation is a good method for estimating parameters with a limited number of samples or none at all. The method’s development is continuously carried out in line with the development of types of data encountered in research. One of developments is in estimating parameters for the case of panel data with auxiliary variables containing measurement errors. This condition is often encountered in the use of survey data. One of most useful surveys in Indonesia about this issue is Susenas or the National Socio-Economic Survey. Since 2015, the Susenas has been implemented in two periods a year, that is in March and September. In March, data is collected with a representative sample size for an estimate at up to the district/city level. As for the Susenas in September, the data collected is less representative for an estimate at up to the provincial level. The September data collection object is part of the March data collection object, thus some repeated sample units are found in the September and March data. A variable of concern in this study is the average consumption per capita that has an asymmetrical distribution. One approach for this case is the lognormal distribution-based modeling. The use of information that has measurement error as an auxiliary variable in the form of a random variable is deemed capable of producing a better estimate. For the repeatedly-obtained data, a first-order autoregressive model approach is applied. In this study, a Small Area Estimation method was developed to handle a small sample size under the repeated data condition, as well as the use of information in the March period as an auxiliary variable with measurement errors.