A new method of robust linear regression analysis: some monte carlo experiments

Sudhanshu Mishra ()

MPRA Paper from University Library of Munich, Germany

Abstract: This paper elaborates on the deleterious effects of outliers and corruption of dataset on estimation of linear regression coefficients by the Ordinary Least Squares method. Motivated to ameliorate the estimation procedure, we have introduced the robust regression estimators based on Campbell’s robust covariance estimation method. We have investigated into two possibilities: first, when the weights are obtained strictly as suggested by Campbell and secondly, when weights are assigned in view of the Hampel’s median absolute deviation measure of dispersion. Both types of weights are obtained iteratively. Using these two types of weights, two different types of weighted least squares procedures have been proposed. These procedures are applied to detect outliers in and estimate regression coefficients from some widely used datasets such as stackloss, water salinity, Hawkins-Bradu-Kass, Hertzsprung-Russell Star and pilot-point datasets. It has been observed that Campbell-II in particular detects the outlier data points quite well (although occasionally signaling false positive too as very mild outliers). Subsequently, some Monte Carlo experiments have been carried out to assess the properties of these estimators. Findings of these experiments indicate that for larger number and size of outliers, the Campbell-II procedure outperforms the Campbell-I procedure. Unless perturbations introduced to the dataset are sizably numerous and very large in magnitude, the estimated coefficients by the Campbell-II method are also nearly unbiased. A Fortan Program for the proposed method has also been appended.

Keywords: Robust regression; Campbell's robust covariance; outliers; Stackloss; Water Salinity; Hawkins-Bradu-Kass; Hertzsprung-Russell Star; Pilot-Plant; Dataset; Monte Carlo; Experiment; Fortran Computer Program (search for similar items in EconPapers)
JEL-codes: C01 C13 C14 C15 C63 (search for similar items in EconPapers)
Date: 2008-07-04
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (3)

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