Review and classi cations of the ridge parameter estimation techniques

Abstract

Ridge parameter estimation techniques under the inffuence of multicollinearityin Linear regression model were reviewed and classiffed intodifferent forms and various types. The different forms are Fixed Maximum(FM), Varying Maximum (VM), Arithmetic Mean (AM), GeometricMean (GM), Harmonic Mean (HM) and Median (M) and thevarious types are Original (O), Reciprocal (R), Square Root (SR) andReciprocal of Square Root (RSR). These classiffcations resulted intoproposing some other techniques of Ridge parameter estimation. Investigationof the existing and proposed ones were done by conducting1000 Monte-Carlo experiments under five (5) levels of multicollinearity(ρ = 0.8, 0.9, 0.95, 0.99, 0.999), three (3) levels of error variance(σ2 = 0.25, 1, 25) and ve levels of sample size (n = 10, 20, 30, 40, 50).The relative eciency (RF ≤ 0.75) of the techniques resulting from theratio of their mean square error and that of the ordinary least squarewas used to compare the techniques.Results show that the proposed techniques perform better than the existingones in some situations; and that the best technique is generallythe ridge parameter in the form of Harmonic Mean, Fixed Maximumand Varying Maximum in their Original and Square Root types.