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Medientyp:
E-Artikel
Titel:
D-OPTIMAL DESIGNS FOR WEIGHTED POLYNOMIAL REGRESSION – A FUNCTIONAL-ALGEBRAIC APPROACH
Beteiligte:
Chang, Fu-Chuen
Erschienen:
Institute of Statistical Science, Academia Sinica and International Chinese Statistical Association, 2005
Erschienen in:Statistica Sinica
Sprache:
Englisch
ISSN:
1017-0405;
1996-8507
Entstehung:
Anmerkungen:
Beschreibung:
<p>This paper is concerned with the problem of computing the approximate D-optimal design for polynomial regression with weight function w(x) > 0 on the design interval I = [m0 − a, m0 + a]. It is shown that w′(x)/w(x) is a rational function on I and a is close to zero, then the problem of constructing D-optimal designs can be transformed into a differential equation problem leading us to a certain matrix including a finite number of auxiliary unknown constants, which can be approximated by a Taylor expansion. We provide a recursive algorithm to compute Taylor expansion of these constants. Moreover, the D-optimal interior support points are the zeros of a polynomial which has coefficients that can be computed from a linear system.</p>