regpro (version 0.1.1)

pcf.single.index: Regression function estimator in the single index model

Description

Computes the values of a single index model regression estimator on a regular grid.

Usage

pcf.single.index(x, y, h, N, kernel="gauss", support=NULL, method="poid",
argd=colMeans(x), type="si")

Arguments

x

n*d data matrix; the matrix of the values of the explanatory variables

y

n vector; the values of the response variable

h

a positive real number; the smoothing parameter of the kernel estimate

N

vector of d positive integers; the number of grid points for each direction

kernel

a character; determines the kernel function; either "gauss" or "uniform"

support

either NULL or a 2*d vector; the vector gives the d intervals of a rectangular support in the form c(low_1,upp_1,...,low_d,upp_d)

method

character string; "poid", "aved", "iter", or "nume"; if method="poid", then the direction vector is estimated using the reference point optionally given in the argument "argd"; if method="aved", then the average derivative method is used; if method="iter", then an iterative algorithm is used; if method="nume", then numerical optimization is used

argd

d vector; the point optionally used in the estimation of the direction vector

type

character string; if type="si", then the direction vector is estimated once, and the same direction vector is used at every grid point, otherwise the estimate of the direction vector may depend on the point of estimation

Value

See Also

single.index,

Examples

set.seed(1)
n<-100
d<-2 
x<-8*matrix(runif(n*d),n,d)-3
C<-(2*pi)^(-d/2)
phi<-function(x){ return( C*exp(-sum(x^2)/2) ) }
D<-3; c1<-c(0,0); c2<-D*c(1,0); c3<-D*c(1/2,sqrt(3)/2)
func<-function(x){phi(x-c1)+phi(x-c2)+phi(x-c3)}
y<-matrix(0,n,1)
for (i in 1:n) y[i]<-func(x[i,])+0.01*rnorm(1)

num<-30  # number of grid points in one direction
pcf<-pcf.single.index(x,y,h=0.5,N=c(num,num))

dp<-draw.pcf(pcf,minval=min(y))
persp(dp$x,dp$y,dp$z,phi=30,theta=-30)
contour(dp$x,dp$y,dp$z,nlevels=30)