# smooth.bibasis: Smooth a discrete surface over a rectangular lattice In fda: Functional Data Analysis

 smooth.bibasis R Documentation

## 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)
``````

### 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.

### 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.

### 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.

`smooth.basis`

fda documentation built on May 29, 2024, 11:26 a.m.