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I understand that the Delta Method can be used to find asymptotic distribution of estimators.

I have a MLE Estimator with

$ E[\hat\Theta] = \frac{n\Theta_0}{n+1} $

$ Var[\hat\Theta] = \frac{\Theta^2_0}{n(n+2)} $

How can I find the asymptotic distribution of this estimator?

Simon Boge Brant
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gts92
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  • Related? https://math.stackexchange.com/questions/2798941/limiting-distribution-of-mle-for-uniform-distribution – Christoph Hanck Jan 22 '20 at 08:10
  • Is this the only available information? You can only say $E[\hat\theta]\to \theta_0$ and $Var[\hat\theta]\to 0$, so $\hat\theta$ converges in probability (and hence in distribution) to $\theta_0$. This of course gives a degenerate asymptotic distribution. – StubbornAtom Jan 22 '20 at 14:35
  • Thank you for your response. The problem provides this info as the mean and variance of MLE of a uniform distribution over [0,$\Theta$]. The problem then asks for an asymptotic distribution for such a MLE estimator. – gts92 Jan 22 '20 at 20:33
  • In that case see https://stats.stackexchange.com/q/130447/119261 for the non-degenerate asymptotic distribution. – StubbornAtom Jan 23 '20 at 13:32
  • See also https://stats.stackexchange.com/a/96689/28746 – Alecos Papadopoulos Nov 02 '20 at 20:23

1 Answers1

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and welcome to stack exchange.

The delta method does not have anything to do with your question.

Maximum likelihood estimators are, under some regularity conditions, asymptically normally distributed.

The delta method is a way of finding the asymptotic distribution of a (differentiable) function of a random variable that is itself asymptotically normal.

Simon Boge Brant
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