The Empirical Best Linear Unbiased Prediction and The Emperical Best Predictor Unit-Level Approaches in Estimating Per Capita Expenditure at the Subdistrict Level

Abstract

Purpose: This study aims to estimate and evaluate per capita expenditure at the subdistrict level in Garut Regency by employing unit-level Small Area Estimation (SAE) techniques, specifically utilizing the Empirical Best Linear Unbiased Predictor (EBLUP) and the Empirical Best Predictor (EBP) methods.

Methods: The data used in this study are socio-economic data, specifically per capita household expenditure in Garut Regency. Socio-economic data generally skew positively rather than the normal distribution, so a method that can approximate or come close to the normal distribution is needed, for example, log-normal transformation. To improve the performance of EBLUP, which may lead to inefficient estimators because of violation of the assumption of normality, this study proposes the Empirical Best Predictor (EBP) method. It handles positively skewed data by applying log-normal transformation to sample data so that it more closely conforms to the desired distribution.

Result: The EBP results are more stable than EBLUP since EBLUP is highly sensitive to outliers, and in cases where the normality assumption is violated, it produces a significant mean square error and inefficient estimators. Evaluating the estimates with both EBLUP and EBP shows Relative Root Mean Squared Error (RRMSE) values above 25%, especially in the subdistricts of Pamulihan, Sukaresmi, and Kersamanah. This is probably due to the household samples being taken in these three subdistricts being comparatively small compared to the other.

Novelty: In this research, we use EBP to improve the performance of EBLUP, which produces inefficient estimators when the normality assumption is violated.