Research ArticleOpen AccessGoogle Scholar indexed
More on the Preliminary Test Stochastic Restricted Liu Estimator in Linear Regression Model
Postgraduate Institute of Science, University of Peradeniya, Peradeniya, Sri Lanka
Department of Statistics & Computer Science, Faculty of Science, University of Peradeniya, Peradeniya, Sri Lanka
Department of Mathematics and Statistics, Faculty of Science, University of Jaffna, Jaffna, Sri Lanka
- 1 Postgraduate Institute of Science, University of Peradeniya, Peradeniya, Sri Lanka
- 2 Department of Statistics & Computer Science, Faculty of Science, University of Peradeniya, Peradeniya, Sri Lanka
- 3 Department of Mathematics and Statistics, Faculty of Science, University of Jaffna, Jaffna, Sri Lanka
Open Journal of Statistics·Volume 05 (2015)·Pages 340–349·Published 22 May 2015·DOI10.4236/ojs.2015.54035
Copy link · social · email
Abstract
In this paper we compare recently developed preliminary test estimator called Preliminary Test Stochastic Restricted Liu Estimator (PTSRLE) with Ordinary Least Square Estimator (OLSE) and Mixed Estimator (ME) in the Mean Square Error Matrix (MSEM) sense for the two cases in which the stochastic restrictions are correct and not correct. Finally a numerical example and a Monte Carlo simulation study are done to illustrate the theoretical findings.
KeywordsMulticollinearityStochastic RestrictionsOrdinary Least Square EstimatorMixed EstimatorPreliminary Test EstimatorMean Square Error Matrix
- Hoerl, E. and Kennard, W. (1970) Ridge Regression: Biased Estimation for Nonorthogonal Problems. Technometrics, 12, 55-67. http://dx.doi.org/10.1080/00401706.1970.10488634
- Liu, K. (1993) A New Class of Biased Estimate in Linear Regression. Communications in Statistics—Theory and Methods, 22, 393-402. http://dx.doi.org/10.1080/03610929308831027
- Akdeniz, F. and Kaçiranlar, S. (1995) On the almost Unbiased Generalized Liu Estimator and Unbiased Estimation of the Bias and MSE. Communications in Statistics—Theory and Methods, 34, 1789-1797. http://dx.doi.org/10.1080/03610929508831585
- Theil, H. and Goldberger. A.S. (1961) On Pure and Mixed Estimation in Economics. International Economic Review, 2, 65-77. http://dx.doi.org/10.2307/2525589
- Hubert, M.H. and Wijekoon, P. (2006) Improvement of the Liu Estimator in Linear Regression Model. Statistical Papers, 47, 471-479. http://dx.doi.org/10.1007/s00362-006-0300-4
- Bancroft, A. (1944) On Biases in Estimation Due to Use of Preliminary Tests of Significance. Annals of Mathematical Statistics, 15, 190-204. http://dx.doi.org/10.1214/aoms/1177731284
- Judge, G. and Bock, E. (1978) The Statistical Implications of Pre-Test and Stein-Rule Estimators in Econometrics. North Holland, New York.
- Wijekoon, P. (1990) Mixed Estimation and Preliminary Test Estimation in the Linear Regression Model. Ph.D. Thesis, University of Dortmund, Dortmund.
- Arumairajan, S. and Wijekoon, P. (2013) Improvement of the Preliminary Test Estimator When Stochastic Restrictions are Available in Linear Regression Model. Open Journal of Statistics, 3, 283-292. http://dx.doi.org/10.4236/ojs.2013.34033
- Gruber. M.H.J. (1998) Improving Efficiency by Shrinkage: The James-Stein and Ridge Regression Estimators. Dekker, Inc., New York.
- Akdeniz, F. and Erol, H. (2003) Mean Squared Error Matrix Comparisons of Some Biased Estimators in Linear Regression. Communications in Statistics—Theory and Methods, 32, 2389-2413. http://dx.doi.org/10.1081/STA-120025385
- Li, Y. and Yang, H. (2010) A New Stochastic Mixed Ridge Estimator in Linear Regression. Statistical Papers, 51, 315-323. http://dx.doi.org/10.1007/s00362-008-0169-5
- Wu, J. and Yang, H. (2013) Two Stochastic Restricted Principal Components Regression Estimator in Linear Regression. Communications in Statistics—Theory and Methods, 42, 3793-3804. http://dx.doi.org/10.1080/03610926.2011.639004