create.basis: Create Basis Set for Functional Data Analysis

Description Details Author(s) References See Also

Description

Functional data analysis proceeds by selecting a finite basis set and fitting data to it. The current fda package supports fitting via least squares penalized with lambda times the integral over the (finite) support of the basis set of the squared deviations from a linear differential operator.

Details

The most commonly used basis in fda is probably B-splines. For periodic phenomena, Fourier bases are quite useful. A constant basis is provided to facilitation arithmetic with functional data objects. To restrict attention to solutions of certain differential equations, it may be useful to use a corresponding basis set such as exponential, monomial or power basis sets.

Power bases support the use of negative and fractional powers, while monomial bases are restricted only to nonnegative integer exponents.

The polygonal basis is essentially a B-spline of order 2, degree 1.

The following summarizes arguments used by some or all of the current create.basis functions:

Author(s)

J. O. Ramsay and Spencer Graves

References

Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

See Also

create.bspline.basis create.constant.basis create.exponential.basis create.fourier.basis create.monomial.basis create.polygonal.basis create.power.basis


fda documentation built on Nov. 17, 2021, 5:14 p.m.