Functional regression with scalar response using non-parametric kernel estimation
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 = r(X) + ε
where the unknown smooth real function r is estimated using kernel estimation by means of
\hat{r}(X)=(∑_i K(d(X,X_i))y_i/h) / (∑_i K(d(X,X_i)/h)) i=1,...,n
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 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@usc.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. 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) ## End(Not run)
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