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

A Partially linear mixed effects model relating a response Y to predictors $ (X,Z,T) $ (X,Z,T) with the mean function $ X<^>{T}\beta +Zb+g(T) $ XT beta+Zb+g(T) 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 beta 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 beta 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.