Optimal estimators in misspecified linear regression model with an application to real-world data

References

• Akdeniz, F., and S. Kairanlar 1995. “On the Almost Unbiased Generalized Liu Estimator and Unbiased Estimation of the Bias and MSE.” Communications in Statistics—Theory and Methods 24 (7):1789–1797. doi: 10.1080/03610929508831585.
   Web of Science ®Google Scholar
• Akdeniz, F., and H. Erol. 2003. “Mean Squared Error Matrix Comparisons of Some Biased Estimators in Linear Regression.” Communications in Statistics-Theory and Methods 2389–2413. doi: doi: 10.1081/STA-120025385.
   Web of Science ®Google Scholar
• Arumairajan, S., and P. Wijekoon. 2015. “Optimal Generalized Biased Estimator in Linear Regression Model.” Open Journal of Statistics 5:403–411. doi: doi: 10.4236/ojs.2015.55042.
   Google Scholar
• Baye, R., and F. Parker. 1984. “Combining Ridge and Principal Component Regression: A Money Demand Illustration.” Communications in Statistics-Theory and Methods 13 (2):197–205. doi: 10.1080/03610928408828675.
   Web of Science ®Google Scholar
• Chandra, S., and G. Tyagi. 2017. “On the Performance of Some Biased Estimators in a Misspecified Model with Correlated Regressors.” Statistics in Transition 18 (1):27–52. doi: doi: 10.21307/stattrans-2016-056.
   Google Scholar
• Gruber, M. 1998. Improving Efficiency by Shrinkage: The James-Stein and Ridge Regression Estimators. New York: CRC Press.
   Google Scholar
• He, D., and Y. Wu. 2014. “A Stochastic Restricted Principal Components Regression Estimator in the Linear Model.” The Scientific World Journal 2014. doi: doi: 10.1155/2014/231506.
   Google Scholar
• Hoerl, A., and R. Kennard. 1970. “Ridge Regression: Biased Estimation for Nonorthogonal Problems.” Technometrics 12:55–67. doi: 10.1080/00401706.1970.10488634.
   Web of Science ®Google Scholar
• Hubert, M., P. Wijekoon. 2004. “Superiority of the Stochastic Restricted Liu Estimator Under Misspecification.” Statistica 64 (1):153–162. doi:http://dx.doi.org/10.6092/issn.1973-2201/29.
   Google Scholar
• Jibo, W., and Y. Hu. 2014. “On the Stochastic Restricted Almost Unbiased Estimators in Linear Regression Model.” Communications in Statistics—Simulation and Computation 428–440. doi:http://dx.doi.org/10.1080/03610918.2012.704540.
   Web of Science ®Google Scholar
• Jibo, W. 2014. “On the Stochastic Restricted r-k Class Estimator and Stochastic Restricted r-d Class Estimator in Linear Regression Model.” Journal of Applied Mathematics. 2014:1–4. doi:http://dx.doi.org/10.1155/2014/173836.
   Google Scholar
• Kaçiranlar, S., and S. Sakalloğlu. 2001. “Combining the Liu Estimator and the Principal Component.” Communications in Statistics—Theory and Methods 30 (12):2699–2705.
   Web of Science ®Google Scholar
• Kadiyala, K. 1986. “Mixed Regression Estimator Under Misspecification.” Economic Letters 21:27–30. doi:http://dx.doi.org/10.1016/0165-1765(86)90115-1. doi: 10.1016/0165-1765(86)90115-1.
   Web of Science ®Google Scholar
• Kayanan, M., and P. Wijekoon, 2017. “Performance of Existing Biased Estimators and the respective Predictors in a Misspecified Linear Regression Model.” Open Journal of Statistics 876–900. doi: doi: 10.4236/ojs.2017.75062.
   Google Scholar
• Kayanan, M., P. Wijekoon, 2018. “Stochastic Restricted Biased Estimators in Misspecified Regression Model with Incomplete Prior Information.” Journal of Probability and Statistics 2018. doi: doi: 10.1155/2018/1452181.
   PubMedGoogle Scholar
• Li, Y., and H.Yang, 2010. “A New Stochastic Mixed Ridge Estimator in Linear Regression Model.” Statistical Papers. 51 (2):315–323. doi: doi: 10.1007/s00362-008-0169-5.
   Web of Science ®Google Scholar
• Liu, K. 1993. “A New Class of Biased Estimate in Linear Regression.” Communication in Statistics—Theory and Methods 22:393–402.
   Web of Science ®Google Scholar
• Massy, F. 1965. “Principal Components Regression in Exploratory Statistical Research.” Journal of the American Statistical Association 60:234–266. doi: 10.1080/01621459.1965.10480787.
   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 70:407–416. doi: 10.1080/01621459.1975.10479882.
   Web of Science ®Google Scholar
• Newhouse, J. P., and S. D. Oman. 1971. An Evaluation of Ridge Estimators. Santa Monica, CA: RAND Corporation.
   Google Scholar
• Rao, C. R., and H. Toutenburg. 1995. Linear Models: Least Squares and Alternatives. 2nd ed. New York: Springer-Verlag.
   Google Scholar
• Mittelhammer, R. C. 1981. “On Specification Error in the General Linear Model and Weak Mean Square Error Superiority of the Mixed Estimator.” Communications in Statistics-Theory and Methods 10 (2):167–176. doi: doi: 10.1080/03610928108828027.
   Web of Science ®Google Scholar
• Ohtani, K., and Y. Honda. 1984. “On Small Sample Properties of the Mixed Regression Predictor Under Misspecification.” Communications in Statistics–Theory and Methods 13 (22):2817–2825. doi: doi: 10.1080/03610928408828863.
   Web of Science ®Google Scholar
• Sarkar, N. 1989. “Comparisons Among Some Estimators In Misspecified Linear Models With Multicollinearity.” Annals of the Institute of Statistical Mathematics 41 (4):717–724. doi: doi: 10.1007/BF00057737.
   Web of Science ®Google Scholar
• Singh, B., Y. P. Chaubey, and T. D. Dwivedi. 1986. “An Almost Unbiased Ridge Estimator.” The Indian Journal of Statistics 48 (3):342–346.
   Google Scholar
• Şiray, G. Ü. 2015. “r-d Class Estimator Under Misspecification.” Communications in Statistics-Theory and Methods 44 (22):4742–4756. doi: doi: 10.1080/03610926.2013.835421.
   Web of Science ®Google Scholar
• Teräsvirta, T. 1980. Linear Restrictions in Misspecified Linear Models and Polynomial Distributed Lag Estimation. Finland: Departntent of Statistics University of Helsinki.
   Google Scholar
• Trenkler, G., and H. Toutenburg. 1990. “Mean Square Error Matrix Comparisons Between Biased Estimators an Overview of Recent Results.” Statistical Papers. 31:165–179. doi: doi: 10.1007/BF02924687.
   Google Scholar
• Trenkler, G., and P. Wijekoon. 1989. “Mean Square Error Matrix Superiority of the Mixed Regression Estimator Under Misspecification.” Statistica.anno. 49 (1):65–71. doi:http://dx.doi.org/10.6092/issn.1973-2201/785.
   Google Scholar
• Theil, H., and A. S. Goldberger. 1961. “On Pure and Mixed Statistical Estimation in Economics.” International Economic Review 2 (1):65–78. doi: doi: 10.2307/2525589.
   Web of Science ®Google Scholar
• Wijekoon, P., and G. Trenkler. 1989. “Mean Square Error Matrix Superiority of Estimators under Linear Restrictions and Misspecification.” Economics Letters 30:141–149. doi:http://dx.doi.org/10.1016/0165-1765(89)90052-9. doi: 10.1016/0165-1765(89)90052-9.
   Web of Science ®Google Scholar
• Wu, J. 2016. “Superiority of the r-k Class Estimator Over Some Estimators in a Misspecified Linear Model.” Communication in Statistics-Theory and Methods 45:1453–1458. doi: doi: 10.1080/03610926.2013.863934.
   Web of Science ®Google Scholar