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Outlier Detection in Multivariate Linear Models Using Lagrange Multipliers

Makkulau1, Edi Cahyono1, Mukhsar1*, Asrul Sani1, La Ode Saidi1, Andi Tenri Ampa1
In statistics, data which deviates so much from other data is called outlier. Outlier can influence the resulting model, hence it can have an impact on decision making. This paper reports a development of the outlier detection method using the Likelihood Displacement Statistic method (LD) and Likelihood Ratio Statistic for a Mean Shift method (LR), called Likelihood Displacement Statistic-Lagrange (LDL) method and Likelihood Ratio Statistic for a Mean Shift method (LR) to the Likelihood Ratio Statistic for a Mean Shift-Lagrange (LRL) method. LDL and LRL method is a method that uses Lagrange multipliers with confidence interval constraint of parameter vector, which is done by deleting m observations and shifting the means on the model using a nonlinear program with Karush-Kuhn Tucker (KKT) condition. This method LDL compares LDL values and Chi-square table values that follow Chi-square distribution, and method LRL compares LRL values and Chi-square table values that follow Chi-square distribution. The advantage of the LDL and LRL method which uses Lagrange multiplier is the optimal values obtained are limited in the determined confidence interval. Since optimal values are limited to this confidence interval. Keywords: Likelihood Displacement Statistic-Lagrange, Likelihood Ratio Statistic for a Mean Shift-Lagrange, Karush-Kuhn Tucker, Outlier, Lagrange Multipliers.

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Diterbitkan pada: • Jurnal: Global Journal of Pure and Applied Mathematics (GJPAM) • ISSN : 0973-1768 (print), 0973-9750 (online) • Vol. 13, Number 6 (2017), pp. 2563-2578 • Terindeks pada: Scimago SJR (Q4, H-Index 5), the Mathematical Reviews, MathSciNet, Zentralblatt MATH and EBSCO Databases, Index Copernicus

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