Performance of Kibria’s methods in partial linear ridge regression model

This paper considers several estimators for estimating the biasing parameter in the study of partial linear models in the presence of multicollinearity. After exhibiting the MSE of ridge estimator based on eigenvalues of design matrix, a simulation study has been conducted to compare the performanceof the estimators. Based on the simulation studywe found that, increasing the correlation between the independent variables has positive effect on the MSE (signal-to-noise-ratio). However, increasingthe value of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\rho $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">ρ</mi> </math> </EquationSource> </InlineEquation> has negative effect on MSE. When the sample size increases the MSE decreases even when the correlation between the independentvariables is large. An application of the proposed model is considered forhousing attributes to illustrate the performance ofdifferent estimators. Copyright Springer-Verlag Berlin Heidelberg 2015