Giorgio Celant and Michel Broniatowski, "Interpolation
and Extrapolation Optimal Designs: Volume 2: Finite
Dimensional General Models"
English | ISBN: 1786300540 | 2017 | 316 pages | PDF | 2
This book considers various extensions of the topics
treated in the first volume of this series, in relation to the
class of models and the type of criterion for optimality.
The regressors are supposed to belong to a generic finite
dimensional Haar linear space, which substitutes for the
classical polynomial case. The estimation pertains to a
general linear form of the coefficients of the model,
extending the interpolation and extrapolation framework;
the errors in the model may be correlated, and the model
may be heteroscedastic. NonÔÇôlinear models, as well as
multivariate ones, are briefly discussed.
The book focuses to a large extent on criteria for
optimality, and an entire chapter presents algorithms
leading to optimal designs in multivariate models. Elfving s
theory and the theorem of equivalence are presented
extensively. The volume presents an account of the
theory of the approximation of real valued functions,
which makes it selfÔÇôconsistent.
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