METHOD THREE empirical benchmarking robust regression (AN EMPIRICAL Comparison OF THREE robust Regression Methods)

University of Lampung

KHOIRIN NISA KHOIRIN Nisa
Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam Department of Mathematics, Faculty of Mathematics and Natural Sciences
Universitas Lampung University of Lampung
Email : adenisa@telkom.net Email: adenisa@telkom.net

ABSTRACT Abstract
Regression analysis is a statistical technique that serves as a basis for drawing inferences about relationship among Regression Statistical analysis is a technique that serves as a basis for drawing inferences about relationship among
variables (Myers, 1990). variables (Myers, 1990). When data contains outlier, a robust technique on regression is urgently needed. When data contains outlier, a robust technique on Regression is urgently needed. In this paper we In this paper we
aim to compare three robust regressions methods: Least Trimmed Square (LTS), Least Median Square (LMS) and Least aim to compare three methods robust regressions: Least Trimmed Square (LTS), Least Median Square (LMS) and Least
Absolute Value (LAV). Absolute Value (LAV). We set a Monte Carlo simulation using 1000 random samples on every sample size we considered: n We set a Monte Carlo simulation using 1000 random samples on every sample size we considered: n
= 30, 60,100, and 200. = 30, 60.100, and 200. We contaminated the data with 10%, 20%, 30% and 40% outliers. We contaminated the data with 10%, 20%, 30% and 40% outliers. The effect of outliers on regression The effect of outliers on Regression
coefficient is studied by comparing the bias, the mean square error (MSE), and the standard error (SE) resulted by LTS, LMS coefficient is studied by comparing the bias, the mean square error (MSE), and the standard error (SE) resulted by LTS, LMS
and LAV in presence of outliers. LAV and in presence of outliers. The result shows that the LMS and LTS yield almost the same bias, MSE and SE. The result shows that the LMS and LTS yield almost the same bias, MSE and SE. And each And each
of the two methods performs better than LAV. of the two methods performs better than LAV.

Keywords: Robust Regression, LTS, LMS, LAV Keywords: robust Regression, LTS, LMS, LAV
http://lemlit.unila.ac.id http://lemlit.unila.ac.id

PEMBANDINGAN EMPIRIS TIGA METODE REGRESI ROBUST (AN EMPIRICAL COMPARISON OF THREE ROBUST REGRESSION METHODS)

Universitas Lampung

KHOIRIN NISA
Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam
Universitas Lampung
Email : adenisa@telkom.net

ABSTRACT
Regression analysis is a statistical technique that serves as a basis for drawing inferences about relationship among
variables (Myers, 1990). When data contains outlier, a robust technique on regression is urgently needed. In this paper we
aim to compare three robust regressions methods: Least Trimmed Square (LTS), Least Median Square (LMS) and Least
Absolute Value (LAV). We set a Monte Carlo simulation using 1000 random samples on every sample size we considered: n
= 30, 60,100, and 200. We contaminated the data with 10%, 20%, 30% and 40% outliers. The effect of outliers on regression
coefficient is studied by comparing the bias, the mean square error (MSE), and the standard error (SE) resulted by LTS, LMS
and LAV in presence of outliers. The result shows that the LMS and LTS yield almost the same bias, MSE and SE. And each
of the two methods performs better than LAV.

Keywords: Robust Regression, LTS, LMS, LAV
http://lemlit.unila.ac.id