On the choice of difference quotients for evaluating prediction intervals
Journal article, 2008

The use of the Gauss approximation formula for prediction intervals of a function of several variables includes the determination of the partial derivatives. In many cases there may be difficulties to find these derivatives and they need to be replaced by difference quotients. The natural choice of step size in such quotients is to make it as small as possible that, however, may lead to numerical problems. Here, it is demonstrated that there is usually no reason for choosing small step sizes. Instead the best choice with respect to linearisation errors is proportional to the standard deviations of the variables involved. It is recommended that the difference quotient should be used with the step size equal to two standard deviations for an approximate 95% prediction interval. © 2007 Elsevier Ltd. All rights reserved.


Thomas Svensson

SP Sveriges Tekniska Forskningsinstitut AB

Jacques de Maré

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Measurement: Journal of the International Measurement Confederation

0263-2241 (ISSN)

Vol. 41 7 755-762

Subject Categories

Computational Mathematics



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