R help - Feb 2005 - loess problems

I have a problem either understanding what loess is doing or that loess
has a problem itself.

As the x-axis variables become more concentrated on a particular point,the
estimated loess tends to zero????. the examples below show what i am
talking about,  why is that? my intution tells me
that it should tend to the mean of the variable which is been smoothed.

Here's a worked up example

x <- c(seq(0,100), rep(100,1000))
y <- rnorm(length(x), mean=10, sd=2)
scatter.smooth(x,y)



Although it does give warnings, I don't understand why it is giving the
estimate as zero.


another example would be

x <- seq(0,100)
y <- rnorm(length(x), mean=50, sd=2)
scatter.smooth(x,y, span=1/length(x))


shoudn't this give just the points at which the smoothing algorithm is
applied?



thank you

The problem is that 90% of your data sit on the boundary.  Loess is a
nearest neighbor smoother (using (100 x span) % of the data to estimate at
each point).  If you call loess() directly with span=2/3 (the default in
scatter.smooth), or something smaller than about 0.91, you'll see that it
has trouble.   

Strangely, if you set span=.8, scatter.smooth() will also complain, but not
at the default span...  (Re-generating the data yet again does trigger the
warnings, so seems like it does catches things some of the time.)

For your second example, I think loess becomes undefined when the span is
set too small (and 1/n is surely too small):  You are asking the algorithm
to take the nearest 1/n of the data to do the smooth.  You would think that
should just mean _the_ nearest data point, but the problem is:
> n <- 100
> 1 / n < 1
[1] TRUE

so you're asking the algoithm to take fewer than 1 data point to estimate at
each point.  The warnings you see for that example is pointing you in the
right direction.

Andy

> From: Jean Eid
> 
> I have a problem either understanding what loess is doing or 
> that loess
> has a problem itself.
> 
> As the x-axis variables become more concentrated on a 
> particular point,the
> estimated loess tends to zero????. the examples below show what i am
> talking about,  why is that? my intution tells me
> that it should tend to the mean of the variable which is been 
> smoothed.
> 
> Here's a worked up example
> 
> x <- c(seq(0,100), rep(100,1000))
> y <- rnorm(length(x), mean=10, sd=2)
> scatter.smooth(x,y)
> 
> 
> 
> Although it does give warnings, I don't understand why it is 
> giving the
> estimate as zero.
> 
> 
> another example would be
> 
> x <- seq(0,100)
> y <- rnorm(length(x), mean=50, sd=2)
> scatter.smooth(x,y, span=1/length(x))
> 
> 
> shoudn't this give just the points at which the smoothing algorithm is
> applied?
> 
> 
> 
> thank you
> 
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