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

## Rabu, 22 Juli 2009

## Senin, 22 Juni 2009

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

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

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