Model identification and selection for varying coefficient errors-in-variables models

In this paper, we proposed a bias-corrected double penalised least squares function method to investigate model identification and selection for varying coefficient errors-in-variables (EV) models. Without making assumptions about whether the regression coefficients in the model are constant or varying coefficients, the proposed method first approximates the nonparametric regression coefficients using a B-spline basis function, then does bias-correction for the unobserved covariates and establishes a double penalised least-squares function to identify, estimate and select the varying and nonzero constant coefficients simultaneously. Under some regularity conditions, the proposed method is consistent in both identification and selection of nonzero constant and varying coefficients. Further, the resulting estimators of varying coefficients possess the optimal convergence rate of nonparametric function estimation, and the estimators of nonzero constant coefficients are consistent and asymptotically normal. Finally, the finite sample performance of the proposed method is evaluated by simulation studies and a real data analysis.