Abstract
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.
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References
Akdeniz F, Erol H (2003) Mean squared error matrix comparisons of some biased estimators in linear regression. Comm Stat Theory Methods 32(12): 2389–2413
Baksalary JK, Trenkler G (1991) Nonnegative and positive definiteness of matrices modified by two matrices of rank one. Linear Algebra Appl 151: 169–184
Durbin J (1953) A note on regression when there is extraneous information about one of the coefficients. J Am Stat Assoc 48: 799–808
Farebrother RW (1976) Further results on the mean square error of ridge regression. J Roy Stat Soc Ser 38(B): 248–250
Gruber MHJ (1998) Improving efficiency by Shrinkage: the James-Stein and ridge regression estimators. Marcel Dekker, Inc., New York
Groß J (2003) Restricted ridge estimation. Stat Prob Lett 65: 57–64
Hoerl AE, Kennard RW (1970) Ridge regression: biased estimation for non-orthogonal problems. Technometrics 12: 55–67
Kaciranlar S, Sakallioglus S, Akdeniz F (1998) Mean squared error comparisons of the modified ridge regression estimator and the restricted ridge regression estimator. Comm Stat Theory Methods 27(1): 131–138
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): 443–459
Liu K. (1993) A new class of biased estimate in linear regression. Comm Stat Theory Methods 22: 393–402
Hubert MH, Wijekoon P (2006) Improvement of the Liu estimator in the linear regression model. Stat Pap 47: 471–479
Rao CR, Toutenburg H (1995) Linear models: least squares and alternatives. Springer, New York
Sarkar N (1992) A new estimator combining the ridge regression and the restricted least squares methods of estimation. Comm Stat Theory Methods 21: 1987–2000
Swindel BF (1976) Good estimators based on prior information. Comm Stat Theory Methods 5: 1065–1075
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 197–206
Theil H, Goldberger AS (1961) On pure and mixed statistical estimation in economics. Intern Econ Rev 2: 65–78
Theil H (1963) On the use of incomplete prior information in regression analysis. J Am Sta Assoc 58: 401–414
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Li, Y., Yang, H. A new stochastic mixed ridge estimator in linear regression model. Stat Papers 51, 315–323 (2010). https://doi.org/10.1007/s00362-008-0169-5
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DOI: https://doi.org/10.1007/s00362-008-0169-5
Keywords
- Ordinary ridge estimator
- Ordinary mixed estimator
- Stochastic mixed ridge estimator
- Mean squared error matrix