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



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.

Suggested Citation

  • Mishra, SK, 2008. "A new method of robust linear regression analysis: some monte carlo experiments," MPRA Paper 9445, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:9445

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    Cited by:

    1. Hock Ann Lim & Habshah Midi, 2016. "Diagnostic Robust Generalized Potential Based on Index Set Equality (DRGP (ISE)) for the identification of high leverage points in linear model," Computational Statistics, Springer, vol. 31(3), pages 859-877, September.
    2. Sudhanshu Kumar MISHRA, 2008. "Robust Two�Stage Least Squares: Some Monte Carlo Experiments," Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 3(4(6)_Wint).
    3. Mishra, SK, 2008. "Robust Two-Stage Least Squares: some Monte Carlo experiments," MPRA Paper 9737, University Library of Munich, Germany.

    More about this item


    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;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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