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A New Method Of Robust Linear Regression Analysis: Some Monte Carlo Experiments

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  • Sudhanshu Kumar MISHRA

Abstract

This paper has elaborated upon 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, it introduces the robust regression estimators based on Campbell's robust covariance estimation method. It investigates 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 and using those 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. Subsequently, some Monte Carlo experiments have been carried out to assess the properties of these estimators whose findings 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 numerous and very large in magnitude, the estimated coefficients are also nearly unbiased.

Suggested Citation

  • Sudhanshu Kumar MISHRA, 2008. "A New Method Of Robust Linear Regression Analysis: Some Monte Carlo Experiments," Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 3(3(5)_Fall), pages 261-268.
  • Handle: RePEc:ush:jaessh:v:3:y:2008:i:3(5)_fall2008:p:261-268
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    Cited by:

    1. Mishra, SK, 2008. "Robust Two-Stage Least Squares: some Monte Carlo experiments," MPRA Paper 9737, University Library of Munich, Germany.
    2. 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.
    3. 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).

    More about this item

    Keywords

    Robust regression; Campbell's robust covariance; outliers; Monte Carlo Experiment; Median absolute Deviation;

    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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