# bifdPar: Define a Bivariate Functional Parameter Object In fda: Functional Data Analysis

 bifdPar R Documentation

## 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)
```

### 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 elseLfdobj <- 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 elseLfdobj <- 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.

### 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

### Source

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009) Functional Data Analysis in 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

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