A new kernel two-parameter prediction under multicollinearity in partially linear mixed measurement error model

Abstract

A Partially linear mixed effects model relating a response Y to predictors $(X,Z,T)$ with the mean function $X^T\text{β}+\mathrm{Zb}+g\left(T\right)$ is considered in this paper. When the parametric parts' variable X are measured with additive error and there is ill-conditioned data suffering from multicollinearity, a new kernel two-parameter prediction method using the kernel ridge and Liu regression approach is suggested. The kernel two parameter estimator of β and the predictor of b are derived by modifying the likelihood and Henderson methods. Matrix mean square error comparisons are calculated. We also demonstrate that under suitable conditions, the resulting estimator of β is asymptotically normal. The situation with an unknown measurement error covariance matrix is handled. A Monte Carlo simulation study, together with an earthquake data example, is compiled to evaluate the effectiveness of the proposed approach at the end of the paper.

COMMUNICATED BY:

• Q. Zhu

Keywords:

• Partially linear mixed model
• measurement error
• multicollinearity
• kernel ridge prediction
• kernel liu prediction

2020 Mathematics Subject Classifications:

• 62J07
• 62G08
• 62J05

Disclosure statement

No potential conflict of interest was reported by the author(s).