Empirical Robust Multivariate Regression Parameter Estimation Using Median Approach

O.K Sajana¹ , T.A Sajesh²

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.5 , pp.65-71, Oct-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i5.6571

Online published on Oct 31, 2018

Copyright © O.K Sajana, T.A Sajesh . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Main purpose of multivariate regression analysis is the estimation of model parameters. The use of maximum likelihood method would not be appropriate in estimation problems while data contains outlier or extreme observations. So it is necessary to find a parameter estimation method in which the value of the estimator is not much affected by small changes in the data. This paper introduces robust method for multivariate regression based on robust estimation of location and scatter matrix of predictor and response variables. In this paper Comedian method is taken as a robust estimator of location and scatter. Based on the simulations, the finite-sample efficiency and robustness of the estimator are investigated. Efficiency of proposed robust estimators is compared with maximum likelihood estimator, minimum covariance determinant estimator and orthogonalized Gnanadesikan-Kettenring estimator in terms of mean squared errors. Proposed estimator combines high robustness and high efficiency in estimation. The proposed method is illustrated on a real data set.

Key-Words / Index Term :
Multivariate Regression, Outliers Detection, Comedian Approach, Finite Sample Efficiency

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