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E-optimal designs for polynomial spline regression

✍ Scribed by Berthold Heiligers

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
145 KB
Volume
75
Category
Article
ISSN
0378-3758

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✦ Synopsis

We give the E-optimal approximate designs for mean (sub-) parameters in dth degree totally positive polynomial spline regression with prescribed knots over an arbitrary compact real interval. Based on a duality between E-and scalar optimality, the optimal design is found to be supported by the extrema of the Chebyshev (i.e., equi-oscillating) spline, with corresponding weights given in terms of certain Lagrange interpolation splines. In particular, for dth degree polynomial regression, parameterized w.r.t. a totally positive basis (e.g. the Bernstein polynomials), we obtain the solution to the E-optimal design problem, where, contrary to the ordinary monomial setup, no restrictions on the size and location of the regression interval or on the particular system of parameters of interest are required.

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