pcf.kernesti.der R Documentation

## A kernel estimator of a partial derivative of a regression function

### Description

Computes the values of an estimator of a partial derivative of a regression function on a regular grid. The estimator is a partial derivative of a kernel regression estimator of the regression function.

### Usage

```pcf.kernesti.der(x, y, h, N, kernel="gauss", support=NULL, direc=1, method="ratio")
```

### 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; the only allowed value is "gauss" `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) `direc` integer 1,...,d; indicates which partial derivative is estimated `method` a character; determines the applied formula in the 1D case

### Value

a piecewise constant function

### Author(s)

Jussi Klemela

`kernesti.der`,

### Examples

```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.kernesti.der(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)
```