A new stochastic mixed ridge estimator in linear regression model
This paper is concerned with the parameter estimation in linear regression model with additional stochastic linear restrictions. To overcome the multicollinearity problem, a new stochastic mixed ridge estimator is proposed and its efficiency is discussed. Necessary and sufficient conditions for the superiority of the stochastic mixed ridge estimator over the ridge estimator and the mixed estimator in the mean squared error matrix sense are derived for the two cases in which the parametric restrictions are correct and are not correct. Finally, a numerical example is also given to show the theoretical results.
KeywordsOrdinary ridge estimator Ordinary mixed estimator Stochastic mixed ridge estimator Mean squared error matrix
Mathematics Subject Classification (2000)62J05 62F30
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- Kaciranlar S, Sakallioglu S, Akdeniz F, Styan GPH, Werner HJ (1999) A new biased estimator in linear regression and a detailed analysis of the widely-analysed dataset on Portland Cement. Sankhya Indian J Stat 61(B): 443–459Google Scholar
- Stein C (1956) Inadmissibility of the usual estimator for mean of multivariate normal distribution. In: Neyman J (ed) Proceedings of the third berkley symposium on mathematical and statistics probability vol 1, pp 197–206Google Scholar