Model detection for functional polynomial regression
A functional polynomial regression model which includes the functional linear model and functional quadratic model as two special cases is considered. In functional polynomial regression, one must balance the costs and benefits of using more parameters in the model. The method of model detection to determine which orders of the polynomial are significant in functional polynomial regression is developed. The proposed methods can identify the true model consistently and have good prediction performances. Numerical studies clearly confirm our theories.
functional polynomial regression model consistency functional principal components adaptive group lasso