New prediction interval and band in the nonlinear regression model : application to predictive modeling in foods
2010
Gauchi , Jean-Pierre (INRA , Jouy-En-Josas (France). UR 0341 Unité de recherche Mathématiques et Informatique Appliquées) | Vila , Jean-Pierre (INRA , Montpellier (France). UMR 0729 Mathématiques, Informatique et Statistique pour l'Environnement et l'Agronomie ) | Coroller , Louis (Université de Bretagne Occidentale, Quimper(France). LUMAQ)
This article is concerned with the proposal of a new prediction interval and band for the nonlinear regression model. The construction principle of this interval and band is based on an exact (the meaning of the term “exact” will be given later) confidence region for parameters of the nonlinear regression model. This region, fully described in Vila and Gauchi (2007), provides a rigorous justification for the new prediction interval and band that we propose. This new band is then compared to the classical bands (which are asymptotic and thus approximate for small n), and also to the band based on the bootstrap resampling method. The comparison of these bands is undertaken with simulated and real data from predictive modeling in food science.
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