bifdPar: Define a Bivariate Functional Parameter Object

Description

Functional parameter objects are used as arguments to functions that estimate functional parameters, such as smoothing functions like smooth.basis. A bivariate functional parameter object supplies the analogous information required for smoothing bivariate data using a bivariate functional data object $x(s,t)$. The arguments are the same as those for fdPar objects, except that two linear differential operator objects and two smoothing parameters must be applied, each pair corresponding to one of the arguments $s$ and $t$ of the bivariate functional data object.

Usage

bifdPar(bifdobj, Lfdobjs=int2Lfd(2), Lfdobjt=int2Lfd(2), lambdas=0, lambdat=0,
      estimate=TRUE)

Value

a bivariate functional parameter object (i.e., an object of class

bifdPar), which is a list with the following components:

bifd: a functional data object (i.e., with class bifd)
Lfdobjs: a linear differential operator object (i.e., with class Lfdobjs)
Lfdobjt: a linear differential operator object (i.e., with class Lfdobjt)
lambdas: a nonnegative real number
lambdat: a nonnegative real number
estimate: not currently used

Arguments

bifdobj

a bivariate functional data object.

Lfdobjs

either a nonnegative integer or a linear differential operator object for the first argument $s$.

If NULL, Lfdobjs depends on bifdobj[['sbasis']][['type']]:

bspline: Lfdobjs <- int2Lfd(max(0, norder-2)), where norder = norder(bifdobj[['sbasis']]).

fourier

Lfdobjs = a harmonic acceleration operator:

Lfdobj <- vec2Lfd(c(0,(2*pi/diff(rngs))^2,0), rngs)

where rngs = bifdobj[['sbasis']][['rangeval']].

anything else

Lfdobj <- int2Lfd(0)

Lfdobjt

either a nonnegative integer or a linear differential operator object for the first argument $t$.

If NULL, Lfdobjt depends on bifdobj[['tbasis']][['type']]:

bspline: Lfdobj <- int2Lfd(max(0, norder-2)), where norder = norder(bifdobj[['tbasis']]).

fourier

Lfdobj = a harmonic acceleration operator:

Lfdobj <- vec2Lfd(c(0,(2*pi/diff(rngt))^2,0), rngt)

where rngt = bifdobj[['tbasis']][['rangeval']].

anything else

Lfdobj <- int2Lfd(0)

lambdas

a nonnegative real number specifying the amount of smoothing to be applied to the estimated functional parameter $x(s,t)$ as a function of $s$..

lambdat

a nonnegative real number specifying the amount of smoothing to be applied to the estimated functional parameter $x(s,t)$ as a function of $t$..

estimate

not currently used.

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.

Examples

Run this code

#See the prediction of precipitation using temperature as
#the independent variable in the analysis of the daily weather
#data, and the analysis of the Swedish mortality data.