Hi Meng-Ying
27 points - you can't really calculate a variogram. With a range of 3 - you have about 9 correlation lenghts in the field. So as a crude approximation, even the standard deviation on the estimate of the mean would be of the order of s.d/sqrt(9) (I vaguely remember trying to get a more accurate version of this in the case of a Gaussian RF as an exercise in one of Matheron's classes...)
so with s.d = 2.8 (or 2.4 ---similar answers), then standard error is 2.8/3=0.9 (approx)
so your confidence interval for the mean would be [m-1.8, m+1.8]
- this is the same order for both the estimate of the sill and for the direct estimate of the variance... both are bad
That is for the comparitively easy case of the mean - The situation for the variance is even worse - so there is no way that you can complain about the quality of the estimate.
I'm not sure if you are suggesting that you should get different answers - or that there is some bias involved but to convince yourself that there is not
repeat your experiment but use a length of 1,000,000 instead of 27....then at least we would get rid of most of the statistical fluctuations - and the estimates should be similar. How are you generating the random sequence - is it an AR process or something where the variance is known theoretically?
Colin
-----Original Message-----
From: Meng-Ying Li [mailto:[EMAIL PROTECTED]]
Sent: Wed 12/8/2004 6:36 PM
To: Digby Millikan
Cc: ai-geostats
Subject: Re: [ai-geostats] Re: Sill versus least-squares classical variance estimate
Hi Digby and All,
I did a little experiment on the idea that Digby mentioned: The sill will
estimate the population variance, but found it not true in my experiment:
1. I generated a set of one-dimentional data with 27 points on regular
unit spacings, which I'd like to take it as the true, or population
value. On purpose, I generate the data so it has an influence range of
three length units.
2. I calculated the experimental variogram. Notice that the variogram is
the population variogram. The sill value is around 2.8.
3. But the population variance is 2.39, lower than the sill value.
This confirms my doubt about using sill value as the estimate of
population variance, since I calculate the variogram and variance based on
all data points. Please tell me what you think. The data I generated are
as follows:
0.056970748
0.14520424
0.849710204
1.650514605
1.101666385
1.015177986
2.150259206
2.830780659
0.223495817
-2.47615958
-3.372697392
-0.530685611
0.786582177
0.970673
0.674755256
0.338461632
1.020874834
0.410936991
1.702892405
2.649748012
4.290179731
3.442015668
1.488818953
0.862788738
0.728709892
2.398182914
1.522546427
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