A comparative Study of Three Improved Robust Regression Procedures.

Dost Muhammad Khan; Sajjad Ahmad Khan; Umair Khalil; Amjad Ali

Author(s)

Dost Muhammad Khan Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan

Sajjad Ahmad Khan Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan

Umair Khalil Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan

Amjad Ali Department of Statistics, Islamia College Peshawar, Peshawar, Pakistan

Abstract

In this study we evaluated three robust regression techniques namely least trimmed square (LTS), least absolute deviation (LTA) and a redescending M-estimator in terms of efficiency and robustness in simple and multiple linear regressions using extensive simulations. The impacts of outlier concentration, geometry and outlying distance in both leverage and residual have been assessed. The simulation scenarios focus on outlier configurations likely to be encountered in practice. The results for each scenario provide insight and restrictions to performance to each procedure. From the simulation results we found that the underlying estimators are robust whenever an acceptable percentage of outliers is present in the data and when it crosses that limit, the robust estimators? breakdown occurs. It is also worth-revealing that no single uniform robust method under study may completely be satisfying all the concerns for regression analysis in the presence of outliers. That is one method may be best for one contamination scenario but might not be good for other. For example, for the full coverage h = n (sample size), LTS perform better than LTA for normal errors and LTA perform better than LTS for Laplace errors. Lastly, we summarize each procedure?s performance and make recommendations.

Publication Details

Page(s) 425-441

DOI DOI not available

Published Journal: Pakistan Journal of Statistics, Volume: 32, Issue: 6, Year: 2016

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