Statistica Sinica 25 (2015), 1547-1566

A NON PARAMETRIC APPROACH FOR CALIBRATION

WITH FUNCTIONAL DATA

Noslen Hernández^{1}, Rolando J. Biscay^{2},

Nathalie Villa-Vialaneix^{3,4} and Isneri Talavera^{1}

Abstract: A new nonparametric approach for statistical calibration with functional data is studied. The practical motivation comes from calibration problems in chemometrics in which a scalar random variable Y needs to be predicted from a functional random variable X. The proposed predictor takes the form of a weighted average of the observed values of Y in the training data set, where the weights are determined by the conditional probability density of X given Y . This functional density, which represents the data generation mechanism in the context of calibration, is so incorporated as a key information into the estimator. The new proposal is computationally simple and easy to implement. Its statistical consistency is proved, and its relevance is shown through simulations and an application to data.

Key words and phrases: Calibration, chemometrics, functional data, Gaussian process, inverse regression.