New Prediction Interval and Band in the Nonlinear Regression Model: Application to Predictive Modeling in Foods |
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| Authors: | Jean-Pierre Gauchi Jean-Pierre Vila Louis Coroller |
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| Institution: | 1. INRA (National Institute of Agronomical Research), Department of Applied Mathematics and Computational Science , Unité MIA , Jouy-en-Josas, France Jean-Pierre.Gauchi@jouy.inra.fr;3. INRA (National Institute of Agronomical Research), Department of Applied Mathematics and Computational Science , UMR Analyse des Systèmes et Biométrie , Montpellier, France;4. Université de Bretagne Occidentale , LUMAQ, Quimper, France |
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| Abstract: | 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
Vila , J.-P. ,
Gauchi , J.-P. ( 2007 ). Optimal designs based on exact confidence regions for parameter estimation of a nonlinear regression model . Journal of Statistical Planning and Inference 137 ( 9 ): 2935 – 2953 .Crossref], Web of Science ®] , Google Scholar]), 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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| Keywords: | Food science Nonlinear regression Parametric confidence region Prediction band Prediction interval Predictive modeling |
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