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I want to compute mean square error (MSE) for a problem but I'm not sure if I'm doing it right.

Suppose that I want to estimate a variable (e.g. the position of an object) like x. The estimation process depends on the realizations of some specific random variables (i.e. Gaussian noises). In order to get accurate results, I know that I have to perform the estimation process N times with different seeds (i.e. different realizations of noises), right?

Lets show the output (the estimated position) of the i'th trial with x_i.

So I have x_1,...,x_N. Assume that we have access to the true value of x which is showed by x_(true).

How should I compute the MSE?

(1) [tex]\frac{1}{N} \sum_{i=1}^{N} (x_{true} - x_i)^2[/tex]

or

(2) [tex](x_{true} - (\frac{1}{N} \sum_{i=1}^{N} x_i))^2[/tex]

Many thanks.

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# Mean square error

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