Review and classications of the ridge parameter estimation techniques

Authors : Adewale F LUKMAN, Kayode AYİNDE

Pages : 953-967

View : 31 | Download : 7

Publication Date : 2017-10-01

Article Type : Research Paper

Abstract :Ridge parameter estimation techniques under the inuence of multi-collinearity in Linear regression model were reviewed and classified into different forms and various types. The different forms are Fixed Maximum insert ignore into journalissuearticles values(FM);, Varying Maximum insert ignore into journalissuearticles values(VM);, Arithmetic Mean insert ignore into journalissuearticles values(AM);, Geometric Mean insert ignore into journalissuearticles values(GM);, Harmonic Mean insert ignore into journalissuearticles values(HM); and Median insert ignore into journalissuearticles values(M); and the various types are Original insert ignore into journalissuearticles values(O);, Reciprocal insert ignore into journalissuearticles values(R);, Square Root insert ignore into journalissuearticles values(SR); and Reciprocal of Square Root insert ignore into journalissuearticles values(RSR);. These classications resulted into proposing some other techniques of Ridge parameter estimation. Investigation of the existing and proposed ones were done by conducting 1000 Monte-Carlo experiments under five insert ignore into journalissuearticles values(5); levels of multicollinearity insert ignore into journalissuearticles values( $\rho=0.8, 0.9, 0.95, 0.99, 0.999$);, three insert ignore into journalissuearticles values(3); levels of error variance insert ignore into journalissuearticles values($\sigma^2=0.25,1,25$); and five levels of sample size insert ignore into journalissuearticles values($n=10,20,30,40,50$);. The relative efficiency insert ignore into journalissuearticles values($RF\leq 0.75$); of the techniques resulting from the ratio of their mean square error and that of the ordinary least square was used to compare the techniques.  Results show that the proposed techniques perform better than the existing ones in some situations; and that the best technique is generally the ridge parameter in the form of Harmonic Mean, Fixed Maximum and Varying Maximum in their Original and Square Root types.
Keywords : Linear Regression Model, Multicollinearity, Ridge Parameter Estimation Techniques, Relative Efficiency