fregre.np | R Documentation |
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),
...
)
fdataobj |
|
y |
Scalar response with length |
h |
Bandwidth, |
Ker |
Type of asymmetric kernel used, by default asymmetric normal kernel. |
metric |
Metric function, by default |
type.S |
Type of smothing matrix |
par.S |
List of parameters for |
... |
Arguments to be passed for |
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
.
Return:
call
: The matched call.
fitted.values
: Estimated scalar response.
H
: Hat matrix.
residuals
: y
minus fitted values
.
df.residual
: 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.
Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@udc.es
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. https://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)
## End(Not run)
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