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Prediction Intervals in Nonlinear Regression
Author(s) -
Pooi A. H.
Publication year - 1991
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710330508
Subject(s) - mathematics , nonlinear system , quadratic equation , transformation (genetics) , nonlinear regression , neighbourhood (mathematics) , least squares function approximation , statistics , regression analysis , mathematical analysis , biochemistry , chemistry , physics , geometry , quantum mechanics , estimator , gene
Abstract By treating the nonlinear model as if it were linear in the parameterization θ in the neighbourhood of the least squares estimate θ, we construct two‐sided nominally‐q‐prediction intervals by applying the usual linear model theory. The derivation of the truncated series expansion of the expected coverage of the prediction intervals at a feasible value of the parameter vector is described. The quadratic approximation of the expected coverage is then obtained for a two‐parameter nonlinear model. Finally we show how we may construct the prediction intervals when a certain type of nonlinear transformation of the parameter vector has been applied.