# fregre.basis.cv: Cross-validation Functional Regression with scalar response... In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

 fregre.basis.cv R Documentation

## Cross-validation Functional Regression with scalar response using basis representation.

### Description

Computes functional regression between functional explanatory variables and scalar response using basis representation.

### Usage

```fregre.basis.cv(
fdataobj,
y,
basis.x = NULL,
basis.b = NULL,
type.basis = NULL,
lambda = 0,
Lfdobj = vec2Lfd(c(0, 0), rtt),
type.CV = GCV.S,
par.CV = list(trim = 0),
weights = rep(1, n),
verbose = FALSE,
...
)
```

### Arguments

 `fdataobj` `fdata` class object. `y` Scalar response with length `n`. `basis.x` Basis for functional explanatory data `fdataobj`. `basis.b` Basis for functional beta parameter. `type.basis` A vector of character string which determines type of basis. By default "bspline". It is only used when `basis.x` or `basis.b` are a vector of number of basis considered. `lambda` A roughness penalty. By default, no penalty `lambda=0`. `Lfdobj` See eval.penalty. `type.CV` Type of cross-validation. By default generalized cross-validation `GCV.S` method. `par.CV` List of parameters for `type.CV`: `trim`, the alpha of the trimming and `draw`. `weights` weights `verbose` If `TRUE` information about the procedure is printed. Default is `FALSE`. `...` Further arguments passed to or from other methods.

### Details

The function `fregre.basis.cv()` uses validation criterion defined by argument `type.CV` to estimate the number of basis elements and/or the penalized parameter (`lambda`) that best predicts the response.

If `basis = NULL` creates bspline basis.

If the functional covariate `fdataobj` is in a format `raw data`, such as matrix or data.frame, creates an object of class `fdata` with default attributes, see `fdata`.

If `basis.x` is a vector of number of basis elements and `basis.b=NULL`, the function force the same number of elements in the basis of `x` and `beta`.

If `basis.x\$type=``fourier''` and `basis.b\$type=``fourier''`, the function decreases the number of fourier basis elements on the min(k.x,k_b), where k.x and k.b are the number of basis element of `basis.x` and `basis.b` respectively.

### Value

Return:

• `fregre.basis` Fitted regression object by the best parameters (basis elements for data and beta and lambda penalty).

• basis.x.opt: Basis used for functional explanatory data estimation `fdata`.

• basis.b.opt: Basis used for for functional `beta` parameter estimation.

• lambda.opt: `lambda` value that minimizes CV or GCV method.

• gcv.opt: Minimum value of CV or GCV method.

### Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@udc.es

### References

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

Febrero-Bande, M., Oviedo de la Fuente, M. (2012). Statistical Computing in Functional Data Analysis: The R Package fda.usc. Journal of Statistical Software, 51(4), 1-28. https://www.jstatsoft.org/v51/i04/

See Also as: `fregre.basis`, `summary.fregre.fd` and `predict.fregre.fd` .
Alternative method: `fregre.pc.cv` and `fregre.np.cv`.

### Examples

```## Not run:
data(tecator)
x<-tecator\$absorp.fdata[1:129]
y=tecator\$y\$Fat[1:129]
b1<-c(15,21,31)
b2<-c(7,9)
res1=fregre.basis.cv(x,y,basis.x=b1)
res2=fregre.basis.cv(x,y,basis.x=b1,basis.b=b2)
res1\$gcv
res2\$gcv
l=2^(-4:10)
res3=fregre.basis.cv(x,y,basis.b=b1,type.basis="fourier",
lambda=l,type.CV=GCV.S,par.CV=list(trim=0.15))
res3\$gcv

## End(Not run)

```

fda.usc documentation built on Oct. 17, 2022, 9:06 a.m.