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I wonder if there is a book talking about profile likelihood in detail, about the parameter computation procedure (grid search, newton-raphson method, EM algorithm); also, about estimation matters: unbiasedness, asymptotic normality, and the profile likelihood confidence interval?

EDIT: I would like to find graduate-level books with technical details

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I dug up my PhD notes since my professor had references for everything. His notes on profile likelihood mainly reference Barndorff-Nielsen and Cox (1994) Inference and Asymptotics, Chapter 3.

I could also provide you with my lecture notes if you are interested.

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  • $\begingroup$ Thank you very much, that was very helpful. I read the part of the book in Chapter 3 and did not find any part talking about the computation. I wonder if you could share with me the notes if it is more thorough about profile likelihood? $\endgroup$
    – wut
    Commented Jun 19, 2021 at 22:11
  • $\begingroup$ send me an email (see my profile) $\endgroup$
    – bdeonovic
    Commented Jun 21, 2021 at 12:16
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I unfortunately don’t know a textbook, but these notes with references by Aaron King and Ed Ionides touch on the topics you mention in the context of partially observed Markov process models. https://kingaa.github.io/short-course/pfilter/pfilter.html. Perhaps they will be a helpful jumping off point!

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  • $\begingroup$ Thank you very much for your time and comment. The note talks pretty clearly about profile likelihood confidence interval :D $\endgroup$
    – wut
    Commented Jun 19, 2021 at 22:13

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