Local Fitting with General Basis Functions.
Collaborative Research Center 386, Discussion Paper 256
Local polynomial modelling can be seen as a local fit of the data against the basis functions 1, x, ... , x^p. In this paper we extend this method to a wide range of other basis functions. We will focus on the power basis, i.e. a basis which consists of the powers of an arbitrary function, and derive an extended Taylor theorem for this basis. We describe the estimation procedure and calculate asymptotic expressions for bias and variance of this local basis estimator. We apply this method to a simulated data set for various basis functions and propose a data-driven method to find a suitable basis function in each situation.