# Some explicit solutions of *c*-optimal design problems for polynomial regression with no intercept

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## Abstract

In this paper, we consider the optimal design problem for extrapolation and estimation of the slope at a given point, say *z*, in a polynomial regression with no intercept. We provide explicit solutions of these problems in many cases and characterize those values of *z*, where this is not possible.

## Keywords

Polynomial regression Extrapolation Slope estimation*c*-optimal designs

## Notes

### Acknowledgements

This work has been supported in part by the Collaborative Research Center “Statistical modeling of nonlinear dynamic processes” (SFB 823, Teilprojekt C2) of the German Research Foundation (DFG). The work of Viatcheslav Melas and Petr Shpilev was partly supported by Russian Foundation for Basic Research (Project No. 20-01-00096). The authors thank Martina Stein, who typed parts of this manuscript with considerable technical expertise. The authors are also grateful to two referees and an associate editor for their constructive comments on an earlier version of this paper.

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