ARTICLE
ABSTRACT
In this article, a modified two-parameter estimator is introduced for the vector of parameters in the linear regression model when data exists with multicollinearity. The properties of the proposed estimator are discussed and the performance in terms of the matrix mean square error criterion over the ordinary least squares (OLS) estimator, a new two-parameter estimator (NTP), an almost unbiased two-parameter estimator (AUTP) and other well known estimators reviewed in this article is investigated. A numerical example and simulation study are finally conducted to illustrate the superiority of the proposed estimator.
KEYWORDS
liu estimator, multicollinearity, two-parameter estimator, mean squared error matrix
REFERENCES
AKDENIZ, F., EROL, H., (2003). Mean squared error matrix comparisons of some biased estimators in linear regression. Commun. Statist. Theor. Meth. 32(23), 89–2413.
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, 1789–1797.
BATAH, F. S., RAMNATHAN, T., GORE, S. D., (2008). The efficiency of modified jackknife and ridge type regression estimators: a comparison. Surveys in Mathematics and its Applications 24(2), 157–174.
BUONACCORSI, J. P., (1996). A Modified estimating equation approach to correcting for measurement error in regression. Biometrika 83, 433–440.
CROUSE, R. H., JIN, C., HANUMARA, R. C., (1995). Unbiased ridge estimation with prior information and ridge trace. Commun. Statist. Theor. Meth. 24, 2341–2354.
DORUGADE, A. V., KASHID, D. N., (2011). Parameter estimation method in Ridge Regression. Interstat May 2011.
HOERL, A. E., KENNARD, R. W., (1970a). Ridge regression: biased estimation for nonorthogonal problems. Tech. 12, 55–67.
HOERL, A. E., KENNARD, R. W., BALDWIN, K. F., (1975). Ridge regression: Some Simulations. Commun. Statist. 4, 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, 443–459.
KADIYALA, K., (1984). A class almost unbiased and efficient estimators of regression coefficients. Econom. Lett. 16, 293–296.
KIBRIA, B. M., (2003). Performance of some new ridge regression estimators. Commun. Statist. –Simulation 32 (2), 419–435.
LIU, K., (1993). A new class of biased estimate in linear regression. Commun. Statist. Theor. Meth. 22, 393–402.
MASSY, W. F., (1965). Principal components regression in exploratory statistical research. JASA 60, 234–266.
NOMURA, M., (1988). On the almost unbiased ridge regression estimation. Commun. Statist. –Simulation 17(3), 729–743.
MAYER, L. S., WILLKE, T. A., (1973). On biased estimation in linear models. Technometrics 15, 497–508.
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, 2707–2725.
OHTANI, K., (1986). On small sample properties of the almost unbiased generalized ridge estimator. Commun. Statist. Theor. Meth. 15, 1571–1578.
SAKALLIOGLU, S., KACIRANLAR, S., (2008). A new biased estimator based on ridge estimation. Stat Papers 49, 669–689.
STEIN, C., (1956). Inadmissibility of the usual estimator for mean of multivariate normal distribution. Proc. Third Berkeley Symp. Math. Statist. Probab. 1, 197–206.
SWINDEL, B. F., (1976). Good ridge estimators based on prior information. Commun. Statist. Theor. Meth. A5, 1065–1075.
SINGH, B., CHAUBEY, Y. P., (1987). On some improved ridge estimators. Stat Papers 28, 53–67.
YANG, H., CHANG, X., (2010). A New Two-Parameter Estimator in Linear Regression. Commun. Statist. Theor. Meth. 39, 923–934.
WU, J., YANG, H., (2011). Efficiency of an almost unbiased two-parameter estimator in linear regression model. Statistics 47(3), 535–545
