On an elliptical thin-plate spline partially varying-coefficient model

In this work, we study the thin-plate spline partially varying-coefficient models with elliptical contoured errors in order to allow distributions with heavier and lighter tails than the normal ones, such as logistic, Pearson VII, power exponential, and Student-t, to be considered. We develop an estimation process for the parameters of the model based on the doubly penalized likelihood function and using smoothing splines. In addition, an explicit conditional solution for the double penalized maximum likelihood estimators is derived to obtain closed expressions for the variance-covariance matrix of the estimators, effective degrees of freedom of the smooth functions and surfaces, and hat matrix associated with the model. To show the proposed methodology, we analyze the Boston housing data utilizing-plate spline partially varying-coefficient model with normal and Student-t errors. This analysis suggests that the proposed model is helpful when we want to describe the effect of some covariates that vary smoothly as a function of other covariates, geographic referencing, and data with heavy-tailed indications.