XU YUTING, TAO CHANGQI
At present, research on functional regression models is mainly based on the estimation of mean regression. However, mean regression only studies the influence of covariates on the mean position of response variables in the conditional distribution, and cannot reflect the relationship between the two at the tail of the conditional distribution, which can lead to information leakage and be easily affected by outliers. At the same time, there is currently no relevant research on partially functional linear additive models in the spatial dimension. In fact, economic relationships between variables exhibit more nonlinear characteristics in space, and ignoring this nonlinear relationship in spatial lag models can easily lead to model setting errors. To overcome the above shortcomings, this paper combines parametric models and semi parametric models with functional data to propose a new partially functional linear additive spatial lag quantile. Regression model. Furthermore, A tool variable estimation method for the model was constructed based on functional principal component analysis and B-spline approximation. Under some regular conditions, the consistency and asymptotic normality of the model parameter estimates were given, and the optimal convergence speed of the function estimates was obtained. The large sample nature of these estimates was also proved. The model can reflect spatial dependence and the influence of functional data, as well as capture multiple nonlinear effects caused by covariates, reducing the risk of model error, solving the curse of dimensionality, and having high robustness. Finally, numerical simulations and practical applications show that the proposed model and method are effective.
