A Functional Density-Based Nonparametric Approach for Statistical Calibration

In 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 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.