Conditional Distribution Function

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),
  ...
)

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.

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.

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.

Author

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@udc.es

Examples

if (FALSE) { # \dontrun{
# 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)
} # }