Variable selection and estimation of partially functional linear multiple varying coefficient spatial autoregressive model under constraint conditions
摘要
In many fields utilizing regression analysis, prior knowledge about the influence of explanatory variables on the response variable is frequently available and can be formulated as constraints on regression coefficients. This paper investigates variable selection and estimation for partially functional linear multiple varying coefficient spatial autoregressive models under constrained conditions, where explanatory variables encompass both infinite-dimensional functional predictors and scalar covariates. We propose a comprehensive methodology that simultaneously estimates spatial lags of the response variable and explanatory variables in the parametric component while selecting significant non-zero nonparametric components. Our approach integrates B-spline basis expansion, functional principal component analysis, two-stage least squares estimation, and optimization algorithms employing non-convex penalty functions with group-SCAD and group-MCP regularization. Additionally, a hypothesis testing procedure is developed to verify linear constraint satisfaction for regression coefficient vectors. Under appropriate tuning parameter selection, we establish convergence rates for the proposed estimators and demonstrate consistency in variable selection. Monte Carlo simulations evaluate the performance of our estimation procedure and testing methodology, while a practical application to