caa a22 4500 475826647 CHVBK 20180406123830.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1023/A:1004185822838 doi (NATIONALLICENCE)springer-10.1023/A:1004185822838 Convex Optimal Designs for Compound Polynomial Extrapolation [Elektronische Daten] [Holger Dette, Mong-Na Lo Huang] The extrapolation design problem for polynomial regression model on the design space [−1,1] is considered when the degree of the underlying polynomial model is with uncertainty. We investigate compound optimal extrapolation designs with two specific polynomial models, that is those with degrees |m, 2m}. We prove that to extrapolate at a point z, |z| > 1, the optimal convex combination of the two optimal extrapolation designs |ξ m * (z), ξ2m * (z)} for each model separately is a compound optimal extrapolation design to extrapolate at z. The results are applied to find the compound optimal discriminating designs for the two polynomial models with degree |m, 2m}, i.e., discriminating models by estimating the highest coefficient in each model. Finally, the relations between the compound optimal extrapolation design problem and certain nonlinear extremal problems for polynomials are worked out. It is shown that the solution of the compound optimal extrapolation design problem can be obtained by maximizing a (weighted) sum of two squared polynomials with degree m and 2m evaluated at the point z, |z| > 1, subject to the restriction that the sup-norm of the sum of squared polynomials is bounded. The Institute of Statistical Mathematics, 2000 Chebyshev polynomials nationallicence convex combination nationallicence extremal problems for polynomials nationallicence Lagrange interpolation polynomial nationallicence optimal discrimination designs nationallicence Dette Holger Fakultät für Mathematik, Ruhr-Universität Bochum, 44780, Bochum, Germany aut Lo Huang Mong-Na Department of Applied Mathematics, National Sun Yat-sen University, 80424, Kaohsiung, Taiwan R.O.C aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/3(2000-09-01), 557-573 0020-3157 52:3<557 2000 52 10463 https://doi.org/10.1023/A:1004185822838 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004185822838 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dette Holger Fakultät für Mathematik, Ruhr-Universität Bochum, 44780, Bochum, Germany aut NATIONALLICENCE 700 1- Lo Huang Mong-Na Department of Applied Mathematics, National Sun Yat-sen University, 80424, Kaohsiung, Taiwan R.O.C aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/3(2000-09-01), 557-573 0020-3157 52:3<557 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer