fda.usc (version 0.9.4)

fregre.np: Functional regression with scalar response using non-parametric kernel estimation

Description

Computes functional regression between functional explanatory variables and scalar response using kernel estimation.

Usage

fregre.np(fdataobj,y,h=NULL,Ker=AKer.norm,metric=metric.lp,
type.S=S.NW,...)

Arguments

fdataobj

fdata class object.

y

Scalar response with length n.

h

Smoothing parameter or bandwidth.

Ker

Type of asymmetric kernel used, by default asymmetric normal kernel.

metric

Metric function, by default metric.lp.

type.S

Type of smothing matrix S. By default S is calculated by Nadaraya-Watson kernel estimator (S.NW).

...

Arguments to be passed for metric.lp o other metric function.

Value

• Return:
• call
  The matched call.
• fitted.values
  Estimated scalar response.
• H
  Hat matrix.
• residuals
  y minus fitted values.
• df
  The residual degrees of freedom.
• r2
  Coefficient of determination.
• sr2
  Residual variance.
• y
  Response.
• fdataobj
  Functional explanatory data.
• mdist
  Distance matrix between x and newx.
• Ker
  Asymmetric kernel used.
• h.opt
  smoothing parameter or bandwidth.

Details

The distance between curves is calculated using the metric.lp although any other semimetric could be used (see semimetric.basis or semimetric.NPFDA functions). Different asymmetric kernels can be used, see Kernel.asymmetric.

References

Ferraty, F. and Vieu, P. (2006). Nonparametric functional data analysis. Springer Series in Statistics, New York. Hardle, W. Applied Nonparametric Regression. Cambridge University Press, 1994.

See Also

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

Examples

data(tecator)
absorp=tecator$absorp.fdata
ind=1:129
x=absorp[ind,]
y=tecator$y$Fat[ind]

res.np=fregre.np(x,y,Ker=AKer.epa)
summary.fregre.fd(res.np)
res.np2=fregre.np(x,y,Ker=AKer.tri)
summary.fregre.fd(res.np2)

# with other semimetrics.
res.pca1=fregre.np(x,y,Ker=AKer.tri,metri=semimetric.pca,q=1)
summary.fregre.fd(res.pca1)
res.deriv=fregre.np(x,y,metri=semimetric.deriv)
summary.fregre.fd(res.deriv)
x.d2=fdata.deriv(x,nderiv=1,method="fmm",class.out='fdata')
res.deriv2=fregre.np(x.d2,y)
summary.fregre.fd(res.deriv2)
x.d3=fdata.deriv(x,nderiv=1,method="bspline",class.out='fdata')
res.deriv3=fregre.np(x.d3,y)
summary.fregre.fd(res.deriv3)