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Interpolation and Extrapolation Optimal Designs V3: Infinite Dimension Models

Interpolation and Extrapolation Optimal Designs V3: Infinite Dimension Models

Giorgio Celant, Michel Broniatowski

ISBN: 978-1-786-30055-3

Apr 2020, Wiley-ISTE

Select type: Hardcover


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This comprehensive treatise proposes a unified approach, based on the interplay between on optimal designs for interpolation and extrapolation and the theory of the uniform approximation of functions. This self-contained book is intended for statisticians interested in the mathematical basis of optimal planning and for mathematicians interested in the applications of approximation theory. It covers topics developed over a century, unifies concepts and notation, and explores the main results and notions of this area of statistical inference; it states explicit methods for the construction of these designs.

Chapter 1 - Approximation of continuous functions in normed spaces

Chapter 2 - Uniform approximation

Chapter 3 - Constrained polynomial approximation

Chapter 4 - Interpolation and extrapolation designs for the polynomial regression

Chapter 5 - Optimal extrapolation design for the Chebyshev regression

Chapter 6 - Optimal design for linear forms of the parameters in a Chebyshev regression

Chapter 7 -An introduction to extrapolation problems based on observations on a collection of intervals

Chapter 8 - Special topics and extensions

Chapter 9 - Instability of the Lagrange interpolation scheme with respect to measurement errors