Consistent Fixed-Effects Selection in Ultra-high dimensional Linear Mixed Models with Error-Covariate Endogeneity

Recently, applied sciences, including longitudinal and clustered studies in biomedicine require the analysis of ultra-high dimensional linear mixed effects models where we need to select important fixed effect variables from a vast pool available candidates. However, all existing literature assume that covariates random components are independent model error which is often violated (endogeneity) practice. In this paper, first investigate issue with particular focus on selection. We study different types endogeneity regularization methods prove their inconsistencies. Then, propose new profiled focused generalized method moments (PFGMM) approach consistently under 'error-covariate' endogeneity, i.e., presence correlation between covariates. Our proposal proved be oracle consistent probability tending one works well most other type too. Additionally, also illustrate few parameter estimators, those variance components, along variable selection through PFGMM. Empirical simulations an interesting real data example further support claimed utility our proposal.