A functional density-based nonparametric approach for statistical calibration

International audienceIn this paper a new nonparametric functional method is introduced for predicting a scalar random variable $Y$ from a functional random variable $X$. The resulting prediction has the form of a weighted average of the training data set, where the weights are determined by the conditional probability density of $X$ given $Y$, 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 $\mathbb{E}(X|Y=y)$ is required. The new proposal is computationally simple and easy to implement. Its performance is shown through its application to both simulated and real data