single.index R Documentation

## Single index model regression estimator at one point

### Description

Computes the value of a single index model regression estimator at one point.

### Usage

```single.index(x, y, arg=NULL, h=1, kernel="gauss", M=2, method="iter",
vect=FALSE, argd=arg, take=length(y), seed=1)
```

### Arguments

 `x` n*d data matrix; the matrix of the values of the explanatory variables `y` n vector; the values of the response variable `arg` NULL or d vector; the point where the value of the regression function is estimated `h` a positive real number; the smoothing parameter of the kernel estimate `kernel` a character; determines the kernel function; either "gauss" or "uniform" `M` integer >=2; the number of iterations `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 `vect` TRUE or FALSE; internal parameter `argd` d vector; the point optionally used in the estimation of the direction vector `take` positive integer `seed` real number; the seed for the random number generator

### Value

either d vector or a real value; if arg=NULL, then the estimated index is returned, otherwise the estimate at "arg" is returned

### Author(s)

Jussi Klemela

`pcf.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)

single.index(x,y)

arg<-c(0,0)
single.index(x,y,arg=arg)
```