Smoothed Empirical Likelihood Approach to Quantile Differences in Paired Data: A Simulation and Application Study on Indonesian Economic Data

Abstract

This study aims to conduct inference on quantile differences in paired data using the smoothed empirical likelihood (SEL) approach. Conventional mean-based approaches are limited in their ability to handle outliers and are less effective in comprehensively representing changes in distribution. The SEL method addresses the issue of the discontinuity of indicator functions in standard empirical likelihood by integrating kernel-based smoothing techniques, thereby enhancing computational stability and coverage accuracy. Through simulation studies involving various distribution scenarios (normal, exponential, and lognormal), sample sizes, and correlation levels, the performance of SEL is evaluated based on coverage probability and average interval length, compared to bootstrap, t-test, and Wilcoxon test methods. The simulation results demonstrate that SEL consistently yields stable coverage probabilities close to the nominal target and achieves high estimation efficiency with narrow confidence intervals, particularly for skewed data distributions. In an empirical application using Indonesia's Gross Regional Domestic Product (PDRB) data for 2016 and 2025, the SEL method proves to be more robust in representing regional economic dynamics than the mean-based method, which tends to be upwardly biased due to the influence of extreme values in metropolitan provinces. Furthermore, the confidence intervals generated by SEL are almost twice as precise as those from the t-test, making it a more accurate analytical tool for development planning aimed at regional equity.