A Review on the Biasing Parameters of Ridge Regression Estimator in LRM

Authors

  • Madhulika Dube Professor & Head Department of Statistics, M. D. University, Rohtak
  • Isha Research Scholar Department of Statistics M. D. University, Rohtak

DOI:

https://doi.org/10.15415/mjis.2014.31007

Keywords:

Ordinary Least Squares Estimator, Multicollinearity, Ridge Regression, Biasing Parameter, Ridge Parameters

Abstract

Ridge regression is one of the most widely used biased estimators in the presence of multicollinearity, preferred over unbiased ones since they have a larger probability of being closer to the true parametric value. Being the modification of the least squares method it introduces a biasing parameter to reduce the length of the parameter under study. As these biasing parameters depend upon the unknown quantities, extensive work has been carried out by several authors to work out the best one. Owing to the fact that over the years large numbers of biasing parameters have been proposed and studied, this article presents an annotated bibliography along with the review on various biasing parameter available.

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References

A l-Hassan, Y.: Performance of New Ridge Regression Estimators. Journal of the Association of Arab Universities for Basic and Applied Science 9, 23-26 (2010).

A lkhamisi, M.A., Shukur, G.: A Monte Carlo Study of Recent Ridge Parameters. Communication in Statistics-Simulation and Computation 36(3), 535-547 (2007). http://dx.doi.org/10.1080/03610910701208619.

Dempster, Arthur P.: Alternatives to Least Squares in Multiple Regression in D. Kabe and R.P. Gupta (eds.), Multivariate Statistical Inference. Amsterdam North-Holland Publishing Co. 25-40 (1973).

Dorugade, A. V.: New Ridge parameters for Ridge Regression, Journal of the Association of Arab Universities for Basic and Applied Sciences, 1-6(2013).

Dorugade, A. V., Kashid, D.N.: Alternative Method for Choosing Ridge Parameter for Regression. Applied Mathematical Sciences 4(9), 447-456 (2010).

Firinguetti, L: A Generalized Ridge Regression Estimator and its Finite Sample Properties. Communications in Statistics-Theory and Methods 28(5), 1217-1229. (1999). http://dx.doi.org/10.1080/03610929908832353

Frisch, R.: Statistical Confluence Analysis by Means of Complete Regression Systems, Institute of Economics, Oslo University, publ. no. 5(1934).

Gujarati, D.N.: Basic Econometrics, McGraw Hill, New York (1995).

H ocking, R.R., Speed, F.M., Lynn, M.J.: A Class of Biased Estimators in Linear Regression. Technometrics 18 (4), 425-437 (1976). http://dx.doi.org/10.1080/00401706.1976.10489474

H oerl, A.E. and Kennard, R.W.: Ridge Regression Applications to Nonorthogonal Problems. Technometrics 12, 69-82 (1970b). http://dx.doi.org/10.1080/00401706.1970.10488634

H oerl, A.E. and Kennard, R.W. Ridge Regression Biased Estimation for Nonorthogonal Problems. Technometrics 12, 55-67 (1970a). http://dx.doi.org/10.1080/00401706.1970.10488634

H oerl, A. and Kennard, R., Baldwin, K.: Ridge Regression: Some Simulation. Commun. Statist. Theory.Meth. 4,105-123 (1975). http://dx.doi.org/10.1080/03610927508827232

Johnston, J.: Econometrics Methods, McGraw-Hill, Auckland (1987).

Judge G., W. Griffiths, R. Hill, H. Liitkepohl, and T, Lee.: The Theory and Practice of Econometrics, (2d ed.), New York: Wiley (1985). http://dx.doi.org/10.1017/S0266466600011294

K halaf, G., Shukur, G.: Choosing Ridge Parameter for Regression Problem. Communication in Statistics-Theory and Methods 34, 1177-1182 (2005). http://dx.doi.org/10.1081/STA-200056836

K ibria, B.M.G.: Performance of Some New Ridge Regression Estimators. Communications in Statistics-Simulation and Computation. 32(2), 419-435 (2003). http://dx.doi.org/10.1081/SAC-120017499

L awless, J.F., Wang, P.: A Simulation Study of Ridge and Other Regression Estimators. Communications in Statistics-Theory and Methods 14, 1589-1604 (1976).

Maddala, G.S: Introduction to Econometrics, John Wiley & Sons (Asia) Pte.Ltd., Singapore (2005).

McDonald, G.C., Galarneau, D.I.: A Monte Carlo Evaluation of Some Ridge- Type Estimators. Journal of the American Statistical Association 70 (350), 407-412 (1975). http://dx.doi.org/10.1080/01621459.1975.10479882

Muniz, G., Kibria, B.M.G.: On Some Ridge Regression Estimators –An Empirical Comparison. Comm. Stat. Simul. Computation, 38(3), pp 621-630 (2009). http://dx.doi.org/10.1080/03610910802592838

Muniz, G., Kibria, B.M.G., Mansson, K., Shukur, G.: On Developing Ridge Regression Parameters: A Graphical Investigation. SORT. 36(2), 115-138 (2012).

Nomura, Masuo: On the Almost Unbiased Ridge Regression Estimation. Communications in Statistics-Simulation and Computation 17 (3), 729-743 (1988). http://dx.doi.org/10.1080/03610918808812690

Sclove, Stanley: Least Squares with Random Regression Coefficient. Technical Report 87, Department of Economics, Stanford University (1973).

Thisted, Ronald, A.: Ridge Regression, Minimax Estimation, and Empirical Bayes Methods. Technical Report 87, Division of Biostatistics, Stanford University (1976).

Wahba, G., Golub, G.H., Heath, M: Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter. Technometrics 21 (2), 215-223 (1979). http://dx.doi.org/10.1080/00401706.1979.10489751

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Published

2014-09-20

How to Cite

Madhulika Dube, and Isha. 2014. “A Review on the Biasing Parameters of Ridge Regression Estimator in LRM”. Mathematical Journal of Interdisciplinary Sciences 3 (1):73-82. https://doi.org/10.15415/mjis.2014.31007.

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