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Designs for estimating an extremal point of quadratic regression models in a hyperball |
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| Authors: | Viatcheslav B Melas Andrey Pepelyshev and Russell C H Cheng |
| Institution: | (1) Department of Mathematics, St. Petersburg State University, Bibliotechnaya sq., 2, 198904 St. Petersburg, Russia;(2) Department of Mathematics, St. Petersburg State University, Bibliotechnaya sq., 2, 198904 St. Petersburg, Russia;(3) Department of Mathematics, University of Southampton, Highfield, SO17 1BJ Southampton, United Kingdom |
| Abstract: | This paper is devoted to studying optimal designs for estimating an extremal point of a multivariate quadratic regression model in the unit hyperball. The problem of estimating an extremal point is reduced to that of estimating certain parameters of a corresponding nonlinear (in parameters) regression model. For this reduced problem truncated locally D-optimal designs are found in an explicit form. The result is a generalization of the results of Fedorov and Müller (1997) for onedimensional quadratic regression function in the unit segment. Received February 2002 |
| Keywords: | Estimating of an extremum point quadratic regression model truncated locally D-optimal designs equivalence theorems |
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