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I read the following statement online:

A staple of frequentist statistics is the maximal likelihood estimate. This provides a single number which is often interpreted as being the “most likely” value of a statistic. However, presenting such a number is often misleading. The reality of statistics is that uncertainty is always present. All we, as statisticians, can do is quantify it

Is this an accurate statement considering that we have the Method of Support? Can we compute the uncertainty of an MLE?

  • The author's objection has nothing to do with maximum likelihood estimation. He / she is merely pointing out that estimates are uncertain, which is obvious. Also a maximum likelihood estimate is not the most likely value of a statistic, but I'm assuming this is some sort of typo. To answer your question, yes, you can estimate the uncertainty of an MLE by estimating its standard error. – dsaxton Mar 13 '16 at 22:43
  • Nice! Can I get a link to back that claim? –  Mar 13 '16 at 22:50
  • You could start on this site at http://stats.stackexchange.com/questions/88481, http://stats.stackexchange.com/questions/14471, and http://stats.stackexchange.com/questions/68080, which are the top three hits on a Google search for [maximum likelihood standard error](https://www.google.com/search?q=maximum+likelihood+standard+error&ie=utf-8&oe=utf-8). – whuber Mar 13 '16 at 22:56
  • Is `standard error` synonymous for confidence intervals? –  Mar 13 '16 at 23:20
  • @zero No. [Standard error](https://en.wikipedia.org/wiki/Standard_error) (see the first sentence) vs [confidence interval](https://en.wikipedia.org/wiki/Confidence_interval) (see the second sentence) – Glen_b Mar 14 '16 at 03:29

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