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fda (version 6.2.0)

smooth.bibasis: Smooth a discrete surface over a rectangular lattice

Description

Estimate a smoothing function f(s, t) over a rectangular lattice

Usage

smooth.bibasis(sarg, targ, y, fdPars, fdPart, fdnames=NULL, returnMatrix=FALSE)

Value

a list with the following components:

fdobj

a functional data object containing a smooth of the data.

df

a degrees of freedom measure of the smooth

gcv

the value of the generalized cross-validation or GCV criterion. If the function is univariate, GCV is a vector containing the error sum of squares for each function, and if the function is multivariate, GCV is a NVAR by NCURVES matrix.

coef

the coefficient matrix for the basis function expansion of the smoothing function

SSE

the error sums of squares. SSE is a vector or a matrix of the same size as GCV.

penmat

the penalty matrix.

y2cMap

the matrix mapping the data to the coefficients.

Arguments

sarg, targ

vectors of argument values for the first and second dimensions, respectively, of the surface function.

y

an array containing surface values measured with noise

fdPars, fdPart

functional parameter objects for sarg and targ, respectively

fdnames

a list of length 3 containing character vectors of names for sarg, targ, and the surface function f(s, t).

returnMatrix

logical: If TRUE, a two-dimensional is returned using a special class from the Matrix package.

References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), 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

smooth.basis