Abstract
The orthonormal series approach is the primary mathematical tool for approximation, data compression, and presentation of curves used in all statistical applications studied in Chapters 3–7. The core topics are given in the first two sections. Section 2.1 considers series approximations via visualization, and Section 2.2 gives a plain introduction in how fast Fourier coefficients can decay. Among special topics, Section 2.3 is devoted to a more formal discussion of the mathematics of series approximation, and it is highly recommended for study or review. Reading other special sections is optional and can be postponed until they are referred to in the following chapters.
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© 1999 Springer-Verlag New York, Inc.
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(1999). Orthonormal Series and Approximation. In: Nonparametric Curve Estimation. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22638-5_2
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DOI: https://doi.org/10.1007/978-0-387-22638-5_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98740-8
Online ISBN: 978-0-387-22638-5
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