
Computes functional regression between functional explanatory variables and scalar response using kernel estimation.
fregre.np(
fdataobj,
y,
h = NULL,
Ker = AKer.norm,
metric = metric.lp,
type.S = S.NW,
par.S = list(w = 1),
...
)
fdata
class object.
Scalar response with length n
.
Bandwidth, h>0
. Default argument values are provided as the
5%--quantile of the distance between fdataobj
curves, see
h.default
.
Type of asymmetric kernel used, by default asymmetric normal kernel.
Metric function, by default metric.lp
.
Type of smothing matrix S
. By default S
is
calculated by Nadaraya-Watson kernel estimator (S.NW
).
List of parameters for type.S
: w
, the weights.
Arguments to be passed for metric.lp
o other
metric function.
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.
The non-parametric functional regression model can be written as follows Ker
argument), h
is the smoothing
parameter and 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
.
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.
See Also as: fregre.np.cv
,
summary.fregre.fd
and predict.fregre.fd
.
Alternative method: fregre.basis
,cand fregre.pc
.
# 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 {
# }
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