Ashok V. Dorugade
ARTICLE

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ABSTRACT

In this article, two-parameter estimators in linear model with multicollinearity are considered. An alternative efficient two-parameter estimator is proposed and its properties are examined. Furthermore, this was compared with the ordinary least squares (OLS) estimator and ordinary ridge regression (ORR) estimators. Also, using the mean squares error criterion the proposed estimator performs more efficiently than OLS estimator, ORR estimator and other reviewed two-parameter estimators. A numerical example and simulation study are finally conducted to illustrate the superiority of the proposed estimator.

KEYWORDS

multicollinearity, ridge regression, two-parameter estimator, mean squared error

REFERENCES

AKDENIZ, F., KACIRANLAR, S., (1995). On the almost unbiased generalized Liu estimator and unbiased estimation of the bias and MSE, Commun. Statist. Theor. Meth., 24, pp. 1789–1797.

CROUSE, R. H., JIN, C., HANUMARA, R. C., (1995). Unbiased ridge estimation with prior information and ridge trace, Commun. Statist. Theor. Meth., 24, pp. 2341–2354.

DORUGADE, A. V., (2014). Modified Two Parameter Estimator in Linear regression, Statistics in Transition - new series, 15 (1), pp. 23–36.

GRUBER, M. H. J., (1998). Improving efficiency by shrinkage the James–Stein and Ridge regression estimators. Marcell Dekker, NewYork.

HOERL, A. E., (1962). Application of ridge analysis to regression problems, Chemical Engineering Progress., 68, pp. 54–59.

HOERL, A. E., KENNARD, R. W., (1968). On regression analysis and biased estimation, Technometrics, 10, pp. 422–423.

HOERL, A. E., KENNARD, R. W., (1970a). Ridge regression: Biased estimation for non orthogonal problems, Technometrics, 12, pp. 55–67.

HOERL, A. E., KENNARD, R. W., (1970b). Ridge regression: Applications to Nonorthogonal problems, Technometrics, 12, pp. 69–82.

HOERL, A. E., KENNARD, R. W., BALDWIN, K. F., (1975). Ridge regression: Some Simulations, Commun. Statist., 4, pp. 105–123.

KACIRANLAR, S., SAKALLIOGLU, S., AKDENIZ, F., STYAN, G. P. H., WERNER, H. J., (1999). A new biased estimator in linear regression and a detailed analysis of the widely-analysed dataset on Portland Cement, Sankhya Ind. J. Statist., 61, pp. 443–459.

LIU, K., (1993). A new class of biased estimate in linear regression, Commun. Statist. Theor. Meth., 22, pp. 393–402.

LIU, K., (2003). Using Liu-type estimator to combat Collinearity. Commun, Statist. Theor. Meth., 32, pp. 1009–1020.

MCDONALD G. C., GALARNEAU, D. I., (1975). A Monte Carlo evaluation of some ridge-type estimators, J Am Stat Assoc., 20, pp. 407–416.

MONTGOMERY, D. C., PECK, E. A., VINING, G. G., (2006). Introduction to linear regression analysis. John Wiley and Sons, New York.

OZKALE, M. R., KACIRANLAR , S., (2007). The restricted and unrestricted two-parameter estimators, Commun. Statist. Theor. Meth., 36, pp. 2707–2725.

SINGH, B., CHAUBEY, Y. P., (1987). On some improved ridge estimators, Stat Papers, 28, pp. 53–67.

YANG, H., CHANG, X., (2010). A New Two-Parameter Estimator in Linear Regression, Commun. Statist. Theor. Meth., 39, pp. 923–934.

WU, J., YANG, H., (2011). Efficiency of an almost unbiased two-parameter estimator in linear regression model, Statistics., 47 (3), pp. 535–545.

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