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weetabixharry
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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!
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!