Abstract
biased estimation procedures have been proposed as an alternative to least squares, there has been little analysis of the predictive performance of the resulting equations. Therefore, we discuss the predictive performanceof the Two Parameter Ridge (2PR) estimator compared to ordinary least squares, principal components andridge regression estimators. Also, the theoretical results are illustrated by a numerical example and a regionis established where the 2PR estimator is uniformly superior to the other estimators
Keywords
Biased estimation Two Parameter Ridge estimator Multicollinearity Prediction Mean SquareError
References
- Friedman, D. J. and Montgomery, D. C. (1985). Evaluation of the predictive performance of biased regression estimators. Journal of Forecasting, 4, 153–163.
- Hoerl, A. E. and Kennard, R. W. (1970). Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12, 55–76.
- Lipovetsky, S. and Conklin, W. M. (2005). Ridge regression in two parameter solution. Applied Stochastic
- Models in Business and Industry, 21, 525–540. Lipovetsky, S. (2006). Two parameter ridge regression and its convergence to the eventual pairwise model.
- Mathematical and Computer Modelling, 44, 304–318. Lipovetsky, S. (2010). Enhanced ridge regressions. Mathematical and Computer Modelling, 51, 338–348.
- Li Y. and Yang, H. (2014). Efficiency of a stochastic restricted two-parameter estimator in linear regres- sion. Applied Mathematics and Computation, 249, 371–381.
- Massy, W. F. (1965). Principal components regression in exploratory statistical research. Journal of the American Statistical Association, 60, 234–256.
- ¨Ozbey, F. and Ka¸cıranlar, S. (2015). Evaluation of the Predictive Performance of the Liu Estimator.
- Communications in Statistics: Theory and Methods, 44, 1981–1993.
- Toker, S. and Ka¸cıranlar S. (2013). On the performance of two parameter ridge estimator under the mean square error criterion. Applied Mathematics and Computation, 219, 4718–4728. Appendix 1
Abstract
References
- Friedman, D. J. and Montgomery, D. C. (1985). Evaluation of the predictive performance of biased regression estimators. Journal of Forecasting, 4, 153–163.
- Hoerl, A. E. and Kennard, R. W. (1970). Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12, 55–76.
- Lipovetsky, S. and Conklin, W. M. (2005). Ridge regression in two parameter solution. Applied Stochastic
- Models in Business and Industry, 21, 525–540. Lipovetsky, S. (2006). Two parameter ridge regression and its convergence to the eventual pairwise model.
- Mathematical and Computer Modelling, 44, 304–318. Lipovetsky, S. (2010). Enhanced ridge regressions. Mathematical and Computer Modelling, 51, 338–348.
- Li Y. and Yang, H. (2014). Efficiency of a stochastic restricted two-parameter estimator in linear regres- sion. Applied Mathematics and Computation, 249, 371–381.
- Massy, W. F. (1965). Principal components regression in exploratory statistical research. Journal of the American Statistical Association, 60, 234–256.
- ¨Ozbey, F. and Ka¸cıranlar, S. (2015). Evaluation of the Predictive Performance of the Liu Estimator.
- Communications in Statistics: Theory and Methods, 44, 1981–1993.
- Toker, S. and Ka¸cıranlar S. (2013). On the performance of two parameter ridge estimator under the mean square error criterion. Applied Mathematics and Computation, 219, 4718–4728. Appendix 1
Details
| Other ID | JA88SV76GD |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Publication Date | June 1, 2016 |
| Published in Issue | Year 2016 Volume: 9 Issue: 2 |