A Non Bayesian Predictive Approach for Functional Calibration

A non Bayesian predictive approach for statistical calibration with functional data is introduced. This is based on extending to the functional calibration setting the definition of non Bayesian predictive probability density proposed by Harris (1989). The new method is elaborated in detail in case of Gaussian functional linear models. It is shown through numerical simulations that the introduced non Bayesian predictive estimator of the unknown parameter of interest in calibration (commonly, a substance concentration) has negligible bias and compares favorably with the classical estimator, particularly in extrapolation problems. A further advantage of the new approach, which is also briefly illustrated, is that it provides not only point estimates but also a predictive likelihood function that allows the researcher to explore the plausibility of any possible parameter value.