How well do ridge parameter estimators proposed so far perform in terms of normality, outlier detection, and MSE criteria?

References

• Al-Hassan, Y. M. 2010. Performance of a new ridge regression estimator. Journal of the Association of Arab Universities for Basic and Applied Sciences 9 (1):23–6. doi: 10.1016/j.jaubas.2010.12.006.
   Google Scholar
• Alkhamisi, M. A., 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
• Alkhamisi, M. A., and G. Shukur. 2008. Developing ridge parameters for SUR model. Communications in Statistics - Theory and Methods 37 (4):544–64. doi: 10.1080/03610920701469152.
   Web of Science ®Google Scholar
• Alkhamisi, M. A., 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
• Asar, Y., A. Karaibrahimoğlu, and A. Genç. 2014. Modified ridge regression parameters: A comparative Monte Carlo study. Hacettepe Journal of Mathematics and Statistics 43 (5):827–41.
   Web of Science ®Google Scholar
• Asar, Y., and A. Genç. 2017. A note on some new modifications of ridge estimators. Kuwait Journal of Science 44 (3):75–82.
   Web of Science ®Google Scholar
• Batah, F. S. M, and S. D. Gore. 2009. Ridge regression estimator: Combining unbiased and ordinary ridge regression methods of estimation. Surveys in Mathematics and its Applications 4:99–109.
   Google Scholar
• Bhat, S. 2019. Performance of a weighted ridge estimator. International Journal of Agricultural and Statistical Sciences 15 (1):347–54.
   Web of Science ®Google Scholar
• Bhat, S., and R. Vidya. 2014. Improvement on Ridge Regression Estimator, in: Proceedings of National Conference on Statistical Methods and Data Analysis, Mysore, India, 65–71.
   Google Scholar
• Bhat, S., and R. Vidya. 2016. A comparative study on the performance of new ridge estimators. Pakistan Journal of Statistics and Operation Research 12 (2):317–25. doi: 10.18187/pjsor.v12i2.1188.
   Web of Science ®Google Scholar
• Bhat, S., and R. Vidya. 2017. A New Ridge Estimator and İts Performance, in: Proceedings of National Conference on Operations Management, Analytics and Statistical Methods, Mysore, India.
   Google Scholar
• Bhat, S., and R. Vidya. 2020. Performance of ridge estimators based on weighted geometric mean and harmonic mean. Journal of Scientific Research 12 (1):1–13. doi: 10.3329/jsr.v12i1.40525.
   Google Scholar
• Dorugade, A. V. 2014a. New ridge parameters for ridge regression. Journal of the Association of Arab Universities for Basic and Applied Sciences 15 (1):94–9. doi: 10.1016/j.jaubas.2013.03.005.
   Google Scholar
• Dorugade, A. V. 2014b. On comparison of some ridge parameters in ridge regression. Sri Lankan Journal of Applied Statistics 15 (1):31–45. doi: 10.4038/sljastats.v15i1.6792.
   Google Scholar
• Dorugade, A. V. 2016. Improved ridge estimator in linear regression with multicollinearity, heteroscedastic errors and outliers. Journal of Modern Applied Statistical Methods 15 (2):362–81. doi: 10.22237/jmasm/1478002860.
   Web of Science ®Google Scholar
• Dorugade, A. V., and D. N. Kashid. 2010. Alternative method for choosing ridge parameter for regression. Applied Mathematical Sciences 4 (9):447–56.
   Google Scholar
• Frisch, R. 1934. Statistical Confluence Analysis by means of Complete Regression Systems (Publication 5). Oslo: University Institute of Economics.
   Google Scholar
• Gibbons, D. G. 1981. A simulation study of some ridge estimators. Journal of the American Statistical Association. 76 (373):131–9. doi: 10.2307/2287058.
   Web of Science ®Google Scholar
• Göktaş, A., and V. Sevinç. 2016. Two new ridge parameters and a guide for selecting an appropriate ridge parameter in linear regression, Gazi Univ. J. Sci 29 (1):201–11.
   Google Scholar
• Haggag, M. M. M. 2016. A new optimal selection of a ridge regression parameter. International Journal of Applied Mathematics & Statistical Sciences 5 (6):101–32.
   Google Scholar
• Hansen, B. E. 2014. Econometrics. Wisconsin: University of Wisconsin Department of Economics.
   Google Scholar
• Hocking, R. R., F. M. Speed, and M. J. Lynn. 1976. A class of biased estimators in linear regression. Technometrics 18 (4):425–37. doi: 10.2307/1268658.
   Web of Science ®Google Scholar
• Hoerl, A. E., and R. W. Kennard. 1970. Ridge regression: Biased estimaton to nonorthogonal problems. Technometrics 12 (1):69–82. doi: 10.2307/1267352.
   Web of Science ®Google Scholar
• Hoerl, A. E., R. W. Kennard, and K. F. Baldwin. 1975. Ridge regression: Some simulations. Communications in Statistics - Simulation and Computation 4 (2):105–23. doi: 10.1080/03610917508548342.
   Web of Science ®Google Scholar
• Karaibrahimoğlu, A., Y. Asar, and A. Genç. 2016. Some new modifications of Kibria’s and Dorugade’s methods: An application to Turkish GDP data. Journal of the Association of Arab Universities for Basic and Applied Sciences 20 (1):89–99. doi: 10.1016/j.jaubas.2014.08.005.
   Google Scholar
• Khalaf, G. 2012. A proposed ridge parameter to improve the least squares estimator. Journal of Modern Applied Statistical Methods 11 (2):443–9. doi: 10.22237/jmasm/1351743240.
   Google Scholar
• Khalaf, G. 2013. A comparison between biased and unbiased estimators in ordinary least squares regression. Journal of Modern Applied Statistical Methods 12 (2):293–303. doi: 10.22237/jmasm/1383279360.
   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.
   Web of Science ®Google Scholar
• Khalaf, G., and M. Iguernane. 2014. Ridge regression and Ill-conditioning. Journal of Modern Applied Statistical Methods 13 (2):355–63. doi: 10.22237/jmasm/1414815420.
   Google Scholar
• Khalaf, G., and M. Iguernane. 2016. Multicollinearity and a ridge parameter estimation approach. Journal of Modern Applied Statistical Methods 15 (2):400–10. doi: 10.22237/jmasm/1478002980.
   Web of Science ®Google Scholar
• Khalaf, G., K. Månsson, 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
• Kibria, B. M. G, and A. F. Lukman. 2020. A new ridge-type estimator for the linear regression model: Simulations and applications. Scientifica 2020:9758378–16. doi: 10.1155/2020/9758378.
   PubMed Web of Science ®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. 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
• Kibria, B. M. G. 2022. More than hundred (100) estimators for estimating the shrinkage parameter in a linear and generalized linear ridge regression models. J. Econom. Stat 2 (2):233–52.
   Google Scholar
• Kibria, B. M. G., K. Månsson, and G. Shukur. 2012. Performance of some logistic ridge regression estimators. Computational Economics 40 (4):401–14. doi: 10.1007/s10614-011-9275-x.
   Web of Science ®Google Scholar
• Kim, H. Y. 2013. Statistical notes for clinical researchers: Assessing normal distribution (2) using skewness and kurtosis. Restorative Dentistry & Endodontics 38 (1):52–4. doi: 10.5395/rde.2013.38.1.52.
   PubMedGoogle Scholar
• Lattef M. N., and M. I. Alheety. 2020. Study of some kinds of ridge regression estimators in linear regression model. Tikrit Journal of Pure Science 25(5):130–142. doi: 10.25130/tjps.v25i5.301.
   Google Scholar
• Lawless, J. F., and P. Wang. 1976. A simulation study of ridge and other regression estimators. Communications in Statistics - Theory and Methods 5 (4):307–23. doi: 10.1080/03610927608827353.
   Web of Science ®Google Scholar
• Leys, C., C. Ley, O. Klein, P. Bernard, and L. Licata. 2013. Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median. Journal of Experimental Social Psychology 49 (4):764–6. doi: 10.1016/j.jesp.2013.03.013.
   Web of Science ®Google Scholar
• Lukman, A. F., and A. Olatunji. 2018. Newly proposed estimator for ridge parameter: An application to the Nigerian economy. Pak. J. Stat 34 (2):91–8.
   Google Scholar
• Lukman, A. F., and K. Ayinde. 2017. Review and classifications of the ridge parameter estimation techniques. Hacettepe Journal of Mathematics and Statistics 46 (113):1–968. doi: 10.15672/HJMS.201815671.
   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
• Lukman, A. F., O. A. Oluyemi, O. B. Akanbi, and O. A. Clement. 2018. Classification-based ridge estimation techniques of Alkhamisi methods. J. Probab. Stat. Sci. 16 (2):165–81.
   Google Scholar
• Månsson, K., and G. Shukur. 2011. On ridge parameters in logistic regression. Communications in Statistics - Theory and Methods 40 (18):3366–81. doi: 10.1080/03610926.2010.500111.
   Web of Science ®Google Scholar
• Mermi, S., A. Göktaş, and Ö. Akkuş. 2021. Are most proposed ridge parameter estimators skewed and do they have any effect on MSE values? Journal of Statistical Computation and Simulation. 91 (10):2074–93. doi: 10.1080/00949655.2021.1883611.
   Web of Science ®Google Scholar
• Montgomery, D. C., E. A. Peck, and G. G. Vining. 2012. Introduction to linear regression analysis. New Jersey: John Wiley & Sons.
   Google Scholar
• Muniz, G., and B. M. G. Kibria. 2009. On some ridge regression estimators: An empirical comparisons. Communications in Statistics - Simulation and Computation 38 (3):621–30. doi: 10.1080/03610910802592838.
   Web of Science ®Google Scholar
• Muniz, G., B. M. G. Kibria, K. Mansson, and G. Shukur. 2012. On developing ridge regression parameters: A graphical investigation. Stat. Oper. Res. Trans 36 (2):115–38.
   Web of Science ®Google Scholar
• Neter, J., W. Wasserman, and M. H. Kutner. 1983. Applied Linear Regression Models. Illinois: Richard D. Irwin, Inc.
   Google Scholar
• Nomura, M. 1988. On the almost unbiased ridge regression estimator. Communications in Statistics - Simulation and Computation 17 (3):729–43. doi: 10.1080/03610918808812690.
   Web of Science ®Google Scholar
• Qasim, M., K. Månsson, and B. M. Golam Kibria. 2021. On some beta ridge regression estimators: Method, simulation and application. Journal of Statistical Computation and Simulation. 91 (9):1699–712. doi: 10.1080/00949655.2020.1867549.
   Web of Science ®Google Scholar
• Saleh, A. K. M. E., M. Arashi, and B. M. G. Kibria. 2019. Theory of ridge regression estimation with applications. New Jersey: John Wiley & Sons.
   Google Scholar
• Suhail, M., M. Ilyas, and A. Ullah. 2019. Modified ridge regression estimators: a simulation study, in: Proceedings of 15th Islamic Countries Conference on Statistical Sciences, ISOSS, Lahore pp. 21-24.
   Google Scholar
• Thisted, R. A. 1976. Ridge regression, minimax estimation, and empirical bayes methods. Stanford: Stanford University.
   Google Scholar
• Ullah, A., M. Suhail, and M. Ilyas. 2017. Modified method for choosing ridge parameter. Journal of Statistical 24:20–34.
   Google Scholar
• Venables, W. N., and B. D. Ripley. 2002. Modern applied statistics with S. New York: Springer Science + Business Media LLC.
   Google Scholar
• West, S. G., J. F. Finch, and P. J. Curran. 1995. Structural equation models with nonnormal variables: Problems and remedies. In Structural equation modeling: concepts, ıssues, and applications, edited by R.H. Hoyle, 56–75. Thousand Oaks: Sage Publications Inc.
   Google Scholar