|Oct21-10, 10:17 AM||#1|
Statistical "Error" of Centroid of Gaussian Distribution
If I have L data samples, distributed randomly (3D real Gaussian distibution, unity variance) about the origin in 3D real space, how can I derive an expression for the "origin estimation error" (i.e. the distance between the true origin and the centroid of the data points) as a function of L?
Intuitively, as L->infinity, the error->0. In fact, it is easy to show in Matlab that the error falls as 1/sqrt(L) (for sufficiently large number of trials). However, I don't know where to start with a proof. (I'm really trying to write a proof for N-dim complex space, but I expect that will only need an extra sqrt(2) term).
Any advice is much appreciated!
|Oct21-10, 11:02 AM||#2|
Of course, I'm simply looking for the standard deviation of the mean. A proof for its behaviour as a function of number of samples can be found in:
J.R. Taylor, "An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements", pp. 147-148.
|error, estimation error, gaussian, normal distribution, statistics|
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