How to Specify Basis Systems for Building Functions

  • J.O Ramsay
  • Giles Hooker
  • Spencer Graves
Part of the Use R book series (USE R)


This chapter is primarily about setting up a basis system. The next chapter will discuss the second step of bundling a set of coefficient values with the chosen basis system.

The functions that we wish to model tend to fall into two main categories: periodic and nonperiodic. The Fourier basis system is the usual choice for periodic functions, and the spline basis system (and bsplines in particular) tends to serve well for nonperiodic functions. We go into these two systems in some detail, and the spline basis especially requires considerable discussion. These two systems are often supplemented by the constant and monomial basis systems, and other systems are described more briefly.

A set of functions in both languages are presented for displaying, evaluating and plotting basis systems as well as for other common tasks.


Basis Function Basis System Break Point Spline Function Basis Object 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.OttawaCanada
  2. 2.Department of Biological Statistics & Computational BiologyCornell UniversityIthacaUSA
  3. 3.Productive Systems EngineeringSan JoseUSA

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