Penalized quadratic inference functions estimation of fixed effects partially linear varying coefficient spatial error model

This study introduces a novel fixed effects partially linear varying coefficient spatial error model featuring a correlation structure within individuals. A penalized quadratic inference functions estimation method for unknowns is proposed by employing B-spline to approximate the varying coefficient functions. Under certain regular conditions, the consistency and asymptotic normality of parametric estimators and the optimal convergence rate of nonparametric estimators are derived. Monte Carlo simulation indicates that the estimates perform strongly in finite sample scenarios. Empirical data analysis demonstrates that the model effectively captures the spatial error correlation of CO${}_2$ emissions and diverse factors’ linear and nonlinear influences on CO${}_2$ emissions. The proposed model and estimation method can be useful for researchers in related disciplines.