fda.usc (version 2.1.0)

cond.F: Conditional Distribution Function

Description

Calculate the conditional distribution function of a scalar response with functional data.

Usage

cond.F(
  fdata0,
  y0,
  fdataobj,
  y,
  h = 0.15,
  g = 0.15,
  metric = metric.lp,
  Ker = list(AKer = AKer.epa, IKer = IKer.epa),
  ...
)

Value

• Fc Conditional distribution function.

• y0 Vector of conditional response.

• g Smoothing parameter or bandwidth of explanatory functional data (fdataobj).

• h Smoothing parameter or bandwidth of respone, y.

• x.dist Distance matrix between curves of fdataobj object.

• xy.dist Distance matrix between cuves of fdataobj and fdata0 objects.

Arguments

fdata0

Conditional explanatory functional data of fdata class.

y0

Vector of conditional response with length n.

fdataobj

fdata class object.

y

Vector of scalar response with length nn.

h

Smoothing parameter or bandwidth of response y.

g

Smoothing parameter or bandwidth of explanatory functional data fdataobj.

metric

Metric function, by default metric.lp.

Ker

List of 2 arguments. The fist argument is a character string that determines the type of asymetric kernel (see Kernel.asymmetric). Asymmetric Epanechnikov kernel is selected by default. The second argumentis a string that determines the type of integrated kernel(see Kernel.integrate). Integrate Epanechnikov kernel is selected by default.
.

...

Further arguments passed to or from other methods.

Author

Manuel Febrero-Bande, Manuel Oviedo de la Fuente

Details

If x.dist=NULL the distance matrix between fdata objects is calculated by function passed in metric argument.

References

Ferraty, F. and Vieu, P. (2006). Nonparametric functional data analysis. Springer Series in Statistics, New York.

See Also

See Also as: cond.mode and cond.quantile.

Examples

if (FALSE) {
# Read data
n= 500
t= seq(0,1,len=101)
beta = t*sin(2*pi*t)^2
x = matrix(NA, ncol=101, nrow=n)
y=numeric(n)
x0<-rproc2fdata(n,seq(0,1,len=101),sigma="wiener")
x1<-rproc2fdata(n,seq(0,1,len=101),sigma=0.1)
x<-x0*3+x1
fbeta = fdata(beta,t)
y<-inprod.fdata(x,fbeta)+rnorm(n,sd=0.1) 
prx=x[1:100];pry=y[1:100]
ind=101;ind2=102:110
pr0=x[ind];pr10=x[ind2,]
ndist=61
gridy=seq(-1.598069,1.598069, len=ndist)

# Conditional Function
res1 = cond.F(pr10, gridy, prx, pry,p=1)
res2 = cond.F(pr10, gridy, prx, pry,h=0.3)
res3 = cond.F(pr10, gridy, prx, pry,g=0.25,h=0.3)

plot(res1$Fc[,1],type="l",ylim=c(0,1))
lines(res2$Fc[,1],type="l",col=2)
lines(res3$Fc[,1],type="l",col=3)
}