New quantile based ridge M-estimator for linear regression models with multicollinearity and outliers

References

• Ali, S., H. Khan, I. Shah, M. M. Butt, and M. Suhail. 2019. A comparison of some new and old robust ridge regression estimators. Communications in Statistics - Simulation and Computation. Advance online publication. doi:10.1080/03610918.2019.1597119.
   Web of Science ®Google Scholar
• Alkhamisi, M., G. Khalaf, and G. Shukur. 2006. Some modifications for choosing ridge parameters. Communications in Statistics - Theory and Methods 35 (11):2005–20. doi:10.1080/03610920600762905.
   Web of Science ®Google Scholar
• Alkhamisi, M., and G. Shukur. 2007. A Monte Carlo study of recent ridge parameters. Communications in Statistics - Simulation and Computation 36 (3):535–47. doi:10.1080/03610910701208619.
   Web of Science ®Google Scholar
• Ayanullah, S., M., and Ilyas, M. 2015. Comparative study for choosing ridge parameter. In 13th International Conference on Statistical Sciences, ed. M. Ahmad, Vol. 28, 39–50. Peshawar, Pakistan: ISOSS.
   Google Scholar
• Ayanullah, S., M., and Ilyas, M. 2017. Modified method for choosing ridge parameter. Journal of Statistics 24:20–34.
   Google Scholar
• Ayinde, K., A. F. Lukman, and O. Arowolo. 2015. Robust regression diagnostics of influential observations in linear regression model. Open Journal of Statistics 05 (04):273–83. doi:10.4236/ojs.2015.54029.
   Google Scholar
• Ayinde, K., A. F. Lukman, S. O. Olarenwaju, and M. O. Attah. 2018. Some new adjusted ridge estimators of linear regression model. International Journal of Civil Engineering and Technology (IJCIET) 9 (11):2838–52.
   Google Scholar
• Chatterjee, S., and Hadi, A. S. 2015. Regression analysis by example. Hoboken, NJ: John Wiley & Sons.
   Google Scholar
• Ertaş, H. 2018. A modified ridge M-estimator for linear regression model with multicollinearity and outliers. Communications in Statistics - Simulation and Computation 47 (4):1240–50. doi:10.1080/03610918.2017.1310231.
   Web of Science ®Google Scholar
• Ertaş, H., S. Kaçıranlar, and H. Güler. 2015. Robust Liu-type estimator for regression based on M-estimator. Communications in Statistics - Simulation and Computation 46 (5):1–32. doi:10.1080/03610918.2015.1045077.
   Web of Science ®Google Scholar
• Kibria, B. M. G. 2003. Performance of some new ridge regression estimators. Communications in Statistics - Simulation and Computation 32 (2):419–35. doi:10.1081/SAC-120017499.
   Web of Science ®Google Scholar
• Gujarati, D. N. 2009. Basic econometrics. New York, NY: Tata McGraw-Hill Education.
   Google Scholar
• Gültay, B., and S. Kaçıranlar. 2014. Mean square error comparisons of the alternative estimators for the distributed lag models. Hacettepe Journal of Mathematics and Statistics 44 (35):1–33. doi:10.15672/HJMS.2014357556.
   Google Scholar
• Hampel, F., E. Ronchetti, P. Rousseeuw, and W. Stahel. 1986. Robust statistics. New York, NY: John Wiley& Sons. doi:10.1186/1742-4755-7-12.
   Google Scholar
• Hoerl, A. E., and R. W. Kennard. 1970. Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12 (1):55–67. doi:10.1080/00401706.1970.10488634.
   Web of Science ®Google Scholar
• Huber, P. J. 1981. Robust statistics. Hoboken, NJ: John Wiley & Sons.
   Google Scholar
• Khalaf, G., K. Mansson, and G. Shukur. 2013. Modified ridge regression estimators. Communications in Statistics - Theory and Methods 42 (8):1476–87. doi:10.1080/03610926.2011.593285.
   Web of Science ®Google Scholar
• Khalaf, G., and G. Shukur. 2005. Choosing ridge parameter for regression problems. Communications in Statistics - Theory and Methods 34 (5):1177–82. doi:10.1081/STA-200056836.
   Google Scholar
• Kibria, B. M. G., and S. Banik. 2016. Some ridge regression estimators and their performances. Journal of Modern Applied Statistical Methods 15 (1):206–38. doi:10.22237/jmasm/1462075860.
   Web of Science ®Google Scholar
• Kibria, B. M. G., and A. F. Lukman. 2020. A new ridge-type estimator for the linear regression model: simulations and applications. Scientifica 2020:9758378. doi:10.1155/2020/9758378.
   Web of Science ®Google Scholar
• Lukman, A. F., and A. Kayode. 2017. Review and classifications of the ridge parameter estimation techniques. Hacettepe Journal of Mathematics and Statistics 46 (5):953–67.
   Web of Science ®Google Scholar
• Lukman, A. F., K. Ayinde, and A. S. Ajiboye. 2017. Monte Carlo study of some classification-based ridge parameter estimators. Journal of Modern Applied Statistical Methods 16 (1):428–51. doi:10.22237/jmasm/1493598240.
   Web of Science ®Google Scholar
• McDonald, G. C., and D. I. Galarneau. 1975. A Monte Carlo evaluation of some ridge-type estimators. Journal of the American Statistical Association 70 (350):407–16. doi:10.1080/01621459.1975.10479882.
   Web of Science ®Google Scholar
• Newhouse, J. P., and O. Samuel. 1971. An evaluation of ridge estimators. A report prepared for United States air force project RAND, Santa Monica, CA 90406.
   Google Scholar
• Silvapulle, M. J. 1991. Robust ridge regression based on an M‐estimator. Australian Journal of Statistics 33 (3):319–33. doi:10.1111/j.1467-842X.1991.tb00438.x.
   Google Scholar
• Suhail, M., and Chand, S. 2019. Performance of some new ridge regression estimators. In 2019 13th International Conference on Mathematics, Actuarial Science, Computer Science and Statistics (MACS), Karachi, Pakistan. 1–4. IEEE. doi:10.1109/MACS48846.2019.9024784.
   Google Scholar
• Suhail, M., S. Chand, and B. M. G. Kibria. 2019a. Quantile based estimation of biasing parameters in ridge regression model. Communications in Statistics: Simulation and Computation 0 (0):1–13. doi:10.1080/03610918.2018.1530782.
   Web of Science ®Google Scholar
• Suhail, M., S. Chand, and B. M. G. Kibria. 2019b. Quantile-based robust ridge m-estimator for linear regression model in presence of multicollinearity and outliers. Communications in Statistics - Simulation and Computation 0 (0):1–13. doi:10.1080/03610918.2019.1621339.
   Web of Science ®Google Scholar
• Suhail, M., and Ilyas, M. 2020. Modified ridge regression estimators: a simulation study. In 15th Islamic Countries Conference on Statistical Sciences (ICCS-15), ed. H. Muhammad and K. Shahjahan, 119–44. Lahore, Pakistan: ISOSS. 978-969-8858-25-4.
   Google Scholar
• Wasti, S. E. 2015. Economic survey of Pakistan 2014-15. Islamabad: Government of Pakistan.
   Google Scholar
• Yasin, S., S. Kamal, and M. Suhail. 2021. Performance of some new ridge parameters in two-parameter ridge regression model. Iranian Journal of Science and Technology, Transactions A: Science 45 (1):327–41. doi:10.1007/s40995-020-01019-7.
   Web of Science ®Google Scholar