A SIMULATION STUDY OF FUNCTIONAL DENSITY-BASED INVERSE REGRESSION

Abstract

In this paper a new nonparametric functional regression method is introduced for predicting a scalar random variable Y on the basis of a functional random variable X. The prediction has the form of a weighted average of the training data yi, where the weights are determined by the conditional probability density of X given Y = yi, which is assumed to be Gaussian. In this way such a conditional probability density is incorporated as a key information into the estimator. Contrary to some previous approaches, no assumption about the dimensionality of E(X|Y = y) or about the distribution of X is required. The new proposal is computationally simple and
easy to implement. Its performance is assessed through a simulation study