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Does any one know of a good source for the study of maximum likelihood estimation on a general exponential family of the form $f(x;\theta)=a(\theta)g(x)\exp[{\sum_{i=1}^{k} b_i(\theta)R_i(x)}]$? Any help is greatly appreciated.

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    $\begingroup$ Off the top of my head, Jun Shao's Mathematical Statistics and Lehmann and Casella's Theory of Point Estimation both discuss this, but I don't know if there is a canonical one $\endgroup$
    – jld
    Jan 3, 2018 at 16:30
  • $\begingroup$ @Chaconne. I also came to know about Jun Shao and Lehmann's other books as well. Very helpful. Thank you very much. $\endgroup$
    – Ashok
    Jan 4, 2018 at 11:47

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The references in Chaconne's comment are both good textbooks. The lecture notes by Larry Brown are also a common entry point into the literature.

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    $\begingroup$ Thank you @Lucas Roberts. These lecture notes seem very rigorous and I was expecting such a source. $\endgroup$
    – Ashok
    Jan 4, 2018 at 11:45
  • $\begingroup$ @Ashok, glad you found them useful. If my answer satisfies your question please mark the answer correct. $\endgroup$ Sep 17, 2018 at 18:15
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    $\begingroup$ Sorry, I forgot do so :) $\endgroup$
    – Ashok
    Sep 19, 2018 at 11:39
  • $\begingroup$ @Ashok, no worries. I'm not sure if the community tracks the answered but unchecked posts but they might. It is easy to forget-I come across my own questions I forgot to mark answers correct too :) . $\endgroup$ Sep 19, 2018 at 14:23

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