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Math Help - how do i show this is a consistent estimator?

  1. #1
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    how do i show this is a consistent estimator?

    I have shown that the expected value of \delta (x) is \theta+1

    How possibly can \delta (x) be an consistent estimator?

    Thanks!

    casper
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  2. #2
    MHF Contributor matheagle's Avatar
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    P\left(\left|\hat\theta-\theta\right|>\epsilon\right)= {1\over n} \to 0

    while E\left(\hat\theta-\theta\right)^2=(n)^2{1\over n}+0\left(1-{1\over n}\right)=n\to \infty
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