| kreg {KernGPLM} | R Documentation |
Calculates a kernel regression estimate (univariate or multivariate).
kreg(x, y, bandwidth = NULL, grid = TRUE, p = 2, q = 2,
product = TRUE, sort = TRUE)
x |
n x d matrix, data |
y |
n x 1 vector, responses |
bandwidth |
scalar or 1 x d, bandwidth(s) |
grid |
logical or m x d matrix (where to calculate the regression) |
p |
integer or text, see kernel.function |
q |
integer, see kernel.function |
product |
(if d>1) product or spherical kernel |
sort |
sort the data, necessary to use the DLL code |
The estimator is calculated by Nadaraya-Watson kernel regression. Future extension to local linear (d>1) or polynomial (d=1) estimates is planned.
List with components:
x |
m x d matrix, where regression has been calculated |
y |
m x 1 vector, regression estimates |
bandwidth |
bandwidth used for calculation |
df.residual |
approximate degrees of freedom (residuals) |
rearrange |
if sort=TRUE, index to rearrange x and y to its original order. |
Marlene Mueller
n <- 1000
x <- rnorm(n)
m <- sin(x)
y <- m + rnorm(n)
plot(x,y,col="gray")
o <- order(x); lines(x[o],m[o],col="green")
lines(kreg(x,y),lwd=2)
## two-dimensional
n <- 100
x <- 6*cbind(runif(n), runif(n))-3
m <- function(x1,x2){ 4*sin(x1) + x2 }
y <- m(x[,1],x[,2]) + rnorm(n)
mh <- kreg(x,y)##,bandwidth=1)
grid1 <- unique(mh$x[,1])
grid2 <- unique(mh$x[,2])
biv.reg <- t(matrix(mh$y,length(grid1),length(grid2)))
orig.m <- outer(grid1,grid2,m)
par(mfrow=c(1,2))
persp(grid1,grid2,orig.m,main="Original Function",
theta=30,phi=30,expand=0.5,col="lightblue",shade=0.5)
persp(grid1,grid2,biv.reg,main="Estimated Function",
theta=30,phi=30,expand=0.5,col="lightblue",shade=0.5)
par(mfrow=c(1,1))
## now with normal x, note the boundary problem,
## which can be somewhat reduced by a gaussian kernel
n <- 1000
x <- cbind(rnorm(n), rnorm(n))
m <- function(x1,x2){ 4*sin(x1) + x2 }
y <- m(x[,1],x[,2]) + rnorm(n)
mh <- kreg(x,y)##,p="gaussian")
grid1 <- unique(mh$x[,1])
grid2 <- unique(mh$x[,2])
biv.reg <- t(matrix(mh$y,length(grid1),length(grid2)))
orig.m <- outer(grid1,grid2,m)
par(mfrow=c(1,2))
persp(grid1,grid2,orig.m,main="Original Function",
theta=30,phi=30,expand=0.5,col="lightblue",shade=0.5)
persp(grid1,grid2,biv.reg,main="Estimated Function",
theta=30,phi=30,expand=0.5,col="lightblue",shade=0.5)
par(mfrow=c(1,1))