Abstract
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.
Chapter PDF
Similar content being viewed by others
References
Osborne, C.: Statistical calibration: A review. Int. Stat. Rev. 59, 309–336 (1991)
Martens, H., Naes, T.: Multivariate calibration. Wiley, Chichester (1989)
Brown, P.J.: Measurement, Regression, and Calibration. Clarendon Press, Oxford (1993)
Massart, D.L., Vandeginste, B.G.M., Buydens, L., Jong, S.D., Lewi, P.J., Smeyers-Verbeke, J.: Handbook of Chemometrics and Qualimetrics: Part B. Elsevier Science B. V., The Netherlands (1997)
Lavine, B.K., Workman, J.: Fundamental reviews: Chemometrics. Anal. Chem. 74, 2763–2770 (2002)
Walters, F.H., Rizzuto, G.T.: The calibration problem in statistics and its application to chemistry. Anal. Lett. 21, 2069–2076 (1988)
Ferraty, F., Vieu, P.: Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics). Springer, New York (2006)
Ramsay, J., Silverman, B.: Functional Data Analysis. Springer, Berlin (1997)
Cuevas, A., Febrero, M., Fraiman, R.: Linear functional regression: the case of fixed design and functional response. The Canadian Joumal of Statistics 30, 285–300 (2002)
Hagwood, C.: The calibration problem as an ill-posed inverse problem. J. Stat. Plan. Infer. 31, 179–185 (1992)
Hernández, N., Biscay, R.J., Talavera, I.: A non-bayesian predictive approach for statistical calibration. Journal of Statistical Computation and Simulation 82, 529–545 (2012)
Harris, I.R.: Predictive fit for natural exponential families. Biometrika 76, 675–684 (1989)
Grenander, U.: Abstract Inference. Wiley, New York (1981)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hernández, N., Biscay, R.J., Talavera, I. (2012). A Non Bayesian Predictive Approach for Functional Calibration. In: Alvarez, L., Mejail, M., Gomez, L., Jacobo, J. (eds) Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. CIARP 2012. Lecture Notes in Computer Science, vol 7441. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33275-3_96
Download citation
DOI: https://doi.org/10.1007/978-3-642-33275-3_96
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33274-6
Online ISBN: 978-3-642-33275-3
eBook Packages: Computer ScienceComputer Science (R0)
