Malaysian Journal of Mathematical Sciences, September 2020, Vol. 14, No. 3
On the Robust Parameter Estimation Method for Linear Model with Autocorrelated Errors in the Presence of High Leverage Points and Outliers in the Y-Direction
Ali, D. A. and Midi, H.
Corresponding Email: daahirxy@gmail.com
Received date: 10 May 2019
Accepted date: 12 May 2020
Abstract:
In the existence of autocorrelation problem, the Ordinary Least Squares (OLS) estimates become incompetent. The Cochrane - Orcutt Prais -
Winsten iterative method (COPW) is the most widely used remedial measure to rectify this problem. However, this iterative procedure is
based on the OLS estimates, which is not resistant and easily influenced by high leverage points (outliers in the x-direction) and outliers in the y-direction. The COPW based on MM estimator is developed to remedy both problems of autocorrelation and high leverage points. Nevertheless, MM estimator does not perform well in the presence of bad leverage points. In this paper, we propose to improvise the Cochrane-Orcutt Prais-Winsten iterative method based on GM6 estimator so that autocorrelated errors and high leverage points can be rectified. The performance of the COPW-GM6 is scrutinized widely by Monte Carlo simulation and real example. The results of this study show that the COPW-GM6 is more efficient than the COPW and COPW-MM.
Keywords: Autocorrelation, bad leverage points, Cochrane-Orcutt Prais-Winsten iterative method (COPW), good leverage points, high leverage points (HLPs), outliers
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