[R] loess question

[Saurav Pathak]

Hi All,

I am trying to use loess to smooth a 2D image, and also obtain the 
standard error for every pixel.  I see that the standard error does not 
make sense.  For example, running the following:

library(stats)
x <- array(c(1:100), dim=c(100,100))
y <- t(x)
v <- exp(-((x-50)^2+(y-50)^2)/30^2)
s <- v*0.02
g_noise <- rnorm(10000, mean = 0, sd = s)
f <- v + g_noise
f.loess <- loess(f ~ x + y, span=0.1, data.frame(x=c(x),y=c(y),f=c(f)))
f.predict <- predict(f.loess, data = data.frame(x = c(x), y = c(y), f = 
c(f)), span = 0.1,se=TRUE)
image(1:100,1:100,matrix(f.predict$se,nrow=100))

I get an image of the standard error that has peaks at regular grid 
nodes.  Shouldn't I expect to see roughly the same error that I put in 
(in this case g_noise)?  I notice that the noise peaks move apart for 
higher span values.

Thanks for your help!
Saurav