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I have a question related to: Why is a likelihood-ratio test distributed chi-squared?

On point 2 of @StasK's answer, he states:

The theorem assumes that all the relevant derivatives are non-zero. This can be challenged with some nonlinear problems and/or parameterizations, and/or situations when a parameter is not identified under the null.

  • What derivatives are these?
  • In the case of mixture distributions, when a parameter is not identified under the null, is it possible for the Information matrix to not be invertible? How?
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    $\begingroup$ You should not normally ask questions in comments on other people's questions in any case - generally the correct behavior is to post a new question, so you don't need to excuse yourself for doing that. [Your lack of ability to comment is easily cured by making just one or two good posts (questions or answers). This question may even be sufficient.] $\endgroup$ – Glen_b Mar 19 '14 at 23:51
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    $\begingroup$ Thanks for asking the question in a new thread, rather than trying to use the "Your Answer" field to do so. You may ask as many questions as you need, so long as they are differentiated from each other, & you spell out what it is that you still don't understand based on the previous answers. Since you have done that here, you are using the site appropriately. $\endgroup$ – gung Mar 19 '14 at 23:52
  • $\begingroup$ To expand on my earlier comment, the kind of question that it is appropriate to place in a comment would be a simple request for clarification of a question or answer, e.g. a question like "when you said 'the power curve is monotonic increasing', were you answering only the part about one-tailed tests, or was that meant to apply to both parts?" (to which the answer would usually also be short, like 'yes, that only refers to the one-tailed test case') -- questions requiring extensive responses are generally better placed as new questions, as you did. $\endgroup$ – Glen_b Mar 20 '14 at 0:07

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