A Simulation Study of Functional Density-Based Inverse Regression

Overview & Synopsis

In this paper a new nonparametric functional 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 $y_{i}$, where the weights are determined by the conditional probability density of $X$ given $Y=y_{i}$, 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.