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Math Help - Mean square error proof

  1. #1
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    Nov 2008
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    Mean square error proof

    I am having trouble with this question

    Unbiasedness and small variance are desirable properties of estimators. However, you can imagine situations where
    a trade-off exists between the two: one estimator may be have a small bias but a much smaller variance than
    another, unbiased estimator. The concept of “mean square error” estimator combines the two concepts. Let ˆμ be
    an estimator of μ. Then the mean square error (MSE) is defined as follows:
    MSE(ˆμ) = E [(ˆμ − μ)^2].
    Prove that
    MSE(ˆμ) = (bias)^2 +Var(ˆμ).

    I emailed my professor and he said this

    Hint: subtract and add in E(ˆμ) in E[(ˆμ − μ)^2].

    But I'm not really sure what he means.

    I'd really appreciate any help with this. Thank You.
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  2. #2
    Ond
    Ond is offline
    Junior Member
    Joined
    Feb 2009
    Posts
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    Hi there. This is my take on this:



    Hopefully that will do...?
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