A Comparative Study of M-Estimation and S-Estimation in Robust Regression Models: A Case Study on Crime Rates in Indonesia - Hidayat, Rahmat; Ruliana; Jumriani; Mar'ah, Zakiyah (Universitas Islam Negeri Alauddin Makassar, 2026)
Robust regression is a regression method used to handle outliers in statistical analysis. Robust regression consists of five estimation methods, namely M-estimation (Maximum Likelihood type), LMS estimation (Least Median of Squares), LTS estimation (Least Trimmed Squares), MM estimation (Method of Moments), and S-estimation (Scale). M-estimation is known for having the smallest variance among the estimators, with high efficiency reaching up to 95%, while S-estimation is based on the residual scale of M-estimation and is characterized by a high breakdown point of up to 50%. The 2022 crime rate data in Indonesia contains outliers. According to data from the Central Statistics Agency, there was a drastic increase in crime incidents in 2022, reaching 372,965 reported cases. Therefore, a comparison of robust regression estimation methods was conducted to obtain the best model that explains the factors influencing crime rates in Indonesia. This study employs robust regression using M-estimation and S-estimation with Tukey bisquare weighting. The dependent variable in this study is the number of crimes in Indonesia in 2022, while the independent variables include population density (x₁), open unemployment rate (x₂), number of poor people (x₃), mean years of schooling/MYS (x₄), and labor force participation rate/TPAK (x₅). The results indicate that S-estimation in robust regression provides the best performance among the methods analyzed.