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Mean square error

  1. Jun 24, 2011 #1
    Hi all,

    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.
     
  2. jcsd
  3. Jun 24, 2011 #2

    mathman

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    Science Advisor
    Gold Member

    Equation (1) is the correct formula. One problem with equation (2), which indicates how wrong it can be, is that you could have a sample set with an average equal to the true mean, but with wildly fluctuating terms, leading to zero as your variance estimate.
     
  4. Jun 26, 2011 #3
    Thanks for your help.
     
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