fregre.np

From fda.usc v2.0.1 by Manuel Oviedo de la Fuente

Functional regression with scalar response using non-parametric kernel estimation

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

Keywords: regression

Usage

fregre.np(
  fdataobj,
  y,
  h = NULL,
  Ker = AKer.norm,
  metric = metric.lp,
  type.S = S.NW,
  par.S = list(w = 1),
  ...
)

Arguments

fdataobj: fdata class object.
y: Scalar response with length n.
h: Bandwidth, h>0. Default argument values are provided as the 5%--quantile of the distance between fdataobj curves, see h.default.
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).
par.S: List of parameters for type.S: w, the weights.
…: Arguments to be passed for metric.lp o other metric function.

Details

The non-parametric functional regression model can be written as follows $$y_i =r(X_i)+\epsilon_i$$ where the unknown smooth real function $r$ is estimated using kernel estimation by means of $$\hat{r}(X)=\frac{\sum_{i=1}^{n}{K(h^{-1}d(X,X_{i}))y_{i}}}{\sum_{i=1}^{n}{K(h^{-1}d(X,X_{i}))}}$$ where $K$ is an kernel function (see Ker argument), h is the smoothing parameter and $d$ is a metric or a semi-metric (see metric argument).

The distance between curves is calculated using the metric.lp although any other semimetric could be used (see semimetric.basis or semimetric.NPFDA functions). The kernel is applied to a metric or semi-metrics that provides non-negative values, so it is common to use asymmetric kernels. Different asymmetric kernels can be used, see Kernel.asymmetric.

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.

References

Ferraty, F. and Vieu, P. (2006). Nonparametric functional data analysis. Springer Series in Statistics, 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. http://www.jstatsoft.org/v51/i04/

Hardle, W. Applied Nonparametric Regression. Cambridge University Press, 1994.

Examples

# NOT RUN {
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(res.np)
res.np2=fregre.np(x,y,Ker=AKer.tri)
summary(res.np2)

# with other semimetrics.
res.pca1=fregre.np(x,y,Ker=AKer.tri,metri=semimetric.pca,q=1)
summary(res.pca1)
res.deriv=fregre.np(x,y,metri=semimetric.deriv)
summary(res.deriv)
x.d2=fdata.deriv(x,nderiv=1,method="fmm",class.out='fdata')
res.deriv2=fregre.np(x.d2,y)
summary(res.deriv2)
x.d3=fdata.deriv(x,nderiv=1,method="bspline",class.out='fdata')
res.deriv3=fregre.np(x.d3,y)
summary(res.deriv3)
# }
# NOT RUN {
# }

Documentation reproduced from package fda.usc, version 2.0.1, License: GPL-2

Community examples

Looks like there are no examples yet.