Kernel ridge prediction method in partially linear mixed measurement error model

Abstract

In this article, a new kernel prediction method by using ridge regression approach is suggested to combat multicollinearity and the impacts of its existence on various views of partially linear mixed measurement error model. We derive the necessary and sufficient condition for the superiority of the linear combinations of the predictors in the sense of the matrix mean square error criterion and give the selection of the ridge biasing parameter. The asymptotic normality condition is investigated and the unknown covariance matrix of measurement errors circumstance is handled. A real data analysis together with a Monte Carlo simulation study is made to assess endorsement of the kernel ridge prediction method.

Keywords:

• Asymptotic normality
• Kernel ridge prediction
• Measurement error
• Multicollinearity
• Partially linear mixed model

Notes

1 The abbreviations” Cov. Struc.” and” Est. Met. for Cov. Par.” refer to” Covariance Structures” and” Estimation Methods for Covariance Parameters”.

2 Any two values of k will not be enough to see whether it increases or decreases. Therefore, it should be at least three k values.