PENERAPAN BOOTSTRAP DALAM METODE MINIMUM COVARIANCE DETERMINANT (MCD) DAN LEAST MEDIAN OF SQUARES (LMS) PADA ANALISIS REGRESI LINIER BERGANDA

  • NI PUTU IIN VINNY DAYANTI Faculty of Mathematics and Natural Sciences, Udayana University
  • NI LUH PUTU SUCIPTAWATI Faculty of Mathematics and Natural Sciences, Udayana University
  • MADE SUSILAWATI Faculty of Mathematics and Natural Sciences, Udayana University

Abstract

Ordinary Least Squares (OLS) Method is a good method to estimate regression parameters when there is no violation in classical assumptions, such as the existence of outlier. Outliers can lead to biased parameters estimator, therefore we need a method that can may not affected by the existence of outlier such as Minimum Covariance Determinant (MCD) and Least Median of Squares (LMS). However, the application of this method is less accurate when it is used for small data. To overcome this problem, it was aplicated bootstrap method in MCD and LMS to determine the comparison of bias in parameters which were produced by both methods in dealing outlier in small data. The used bootstrap method in this study was the residual bootstrap that works by resampling the residuals. By using 95% and 99% confidence level and 5%, 10%  and 15% outlier percentage, MCD-bootstrap and LMS-bootstrap give value of parameter estimators which were unbias for all percentage of outlier. We also found that the widht of range which produced by MCD-bootstrap method was shorter than LMS-bootstrap method produced. This indicates that MCD-bootstrap method was a better method than LMS-bootstrap method.

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Author Biographies

NI PUTU IIN VINNY DAYANTI, Faculty of Mathematics and Natural Sciences, Udayana University
Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University
NI LUH PUTU SUCIPTAWATI, Faculty of Mathematics and Natural Sciences, Udayana University
Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University
MADE SUSILAWATI, Faculty of Mathematics and Natural Sciences, Udayana University
Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University
Published
2016-01-30
How to Cite
DAYANTI, NI PUTU IIN VINNY; SUCIPTAWATI, NI LUH PUTU; SUSILAWATI, MADE. PENERAPAN BOOTSTRAP DALAM METODE MINIMUM COVARIANCE DETERMINANT (MCD) DAN LEAST MEDIAN OF SQUARES (LMS) PADA ANALISIS REGRESI LINIER BERGANDA. E-Jurnal Matematika, [S.l.], v. 5, n. 1, p. 22-26, jan. 2016. ISSN 2303-1751. Available at: <https://ojs.unud.ac.id/index.php/mtk/article/view/18717>. Date accessed: 28 mar. 2024. doi: https://doi.org/10.24843/MTK.2016.v05.i01.p116.
Section
Articles

Keywords

outliers; bias; robust; Minimum Covariance Determinant; Least Median of Squares; bootstrap residual

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