Juhyun Park (Lancaster)
Functional average derivative regression
Abstract: Single index model is studied in the framework of regression estimation involving functional data. The model extends a linear model with an unknown link function and has the advantage of having low sensitivity to dimensional effects and flexibility and easiness of interpretation. However its usage in functional regression setting is still found to be limited, partly due to its complexity of fitting the model. In this work we develop a functional adaptation of the average derivative method that allows us to construct an explicit estimator for the functional single index.
Thanks to its explicit form of the estimator, implementation is made relatively simple and straightforward. Theoretical properties of the estimator of the index are studied based on asymptotic results on nonparametric functional derivatives estimation. In particular it is shown that the nonlinear regression component of the model can be estimated at the standard univariate rate, being therefore insensitive to the infinite dimensionality of the data.

Numerical examples are used to illustrate the method and to evaluate finite sample performance.