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Is this a mistake? (regarding maximum likelihood estimator)


Validity of maximising log-likelihood for maximum likelihood estimationMethod of moments and maximum likelihood problemKL-divergence as a negative log likelihood for exponential familiesimprove performance of finding rolling window maximum likelihoodMaximum-Likelihood estimatorMaximum Likelihood Estimators under null hypothesis $H_0: mu=csigma$Finding the maximum likelihood estimatorMaximum likelihood estimator for $theta$Variance of distribution for maximum likelihood estimatorMaximum Likelihood with 2 Samples






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1












$begingroup$


Screenshot from textbook



Under 'general remarks' on maximum likelihood estimators. I don't understand the right hand side of ii. (it is also repeated in iii. this time as the log-likelihood function). That the MLE is theta hat equals arg-theta-max makes sense but why does the likelihood function of theta hat also equal arg-theta-max? Doesn't this imply that theta-hat equals its own likelihood function? This doesn't make sense to me. Should it?










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$endgroup$


















    1












    $begingroup$


    Screenshot from textbook



    Under 'general remarks' on maximum likelihood estimators. I don't understand the right hand side of ii. (it is also repeated in iii. this time as the log-likelihood function). That the MLE is theta hat equals arg-theta-max makes sense but why does the likelihood function of theta hat also equal arg-theta-max? Doesn't this imply that theta-hat equals its own likelihood function? This doesn't make sense to me. Should it?










    share|cite|improve this question







    New contributor



    Awaitingthebus is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.






    $endgroup$














      1












      1








      1





      $begingroup$


      Screenshot from textbook



      Under 'general remarks' on maximum likelihood estimators. I don't understand the right hand side of ii. (it is also repeated in iii. this time as the log-likelihood function). That the MLE is theta hat equals arg-theta-max makes sense but why does the likelihood function of theta hat also equal arg-theta-max? Doesn't this imply that theta-hat equals its own likelihood function? This doesn't make sense to me. Should it?










      share|cite|improve this question







      New contributor



      Awaitingthebus is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






      $endgroup$




      Screenshot from textbook



      Under 'general remarks' on maximum likelihood estimators. I don't understand the right hand side of ii. (it is also repeated in iii. this time as the log-likelihood function). That the MLE is theta hat equals arg-theta-max makes sense but why does the likelihood function of theta hat also equal arg-theta-max? Doesn't this imply that theta-hat equals its own likelihood function? This doesn't make sense to me. Should it?







      maximum-likelihood






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      share|cite|improve this question







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      asked 9 hours ago









      AwaitingthebusAwaitingthebus

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          1 Answer
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          $begingroup$

          I believe the second parts should read
          $$
          L(hattheta) = max_theta L(theta)
          $$

          and
          $$
          l(hattheta) = max_theta l(theta)
          $$



          As written, it doesn't make sense.






          share|cite|improve this answer









          $endgroup$













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            1 Answer
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            active

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            $begingroup$

            I believe the second parts should read
            $$
            L(hattheta) = max_theta L(theta)
            $$

            and
            $$
            l(hattheta) = max_theta l(theta)
            $$



            As written, it doesn't make sense.






            share|cite|improve this answer









            $endgroup$

















              5












              $begingroup$

              I believe the second parts should read
              $$
              L(hattheta) = max_theta L(theta)
              $$

              and
              $$
              l(hattheta) = max_theta l(theta)
              $$



              As written, it doesn't make sense.






              share|cite|improve this answer









              $endgroup$















                5












                5








                5





                $begingroup$

                I believe the second parts should read
                $$
                L(hattheta) = max_theta L(theta)
                $$

                and
                $$
                l(hattheta) = max_theta l(theta)
                $$



                As written, it doesn't make sense.






                share|cite|improve this answer









                $endgroup$



                I believe the second parts should read
                $$
                L(hattheta) = max_theta L(theta)
                $$

                and
                $$
                l(hattheta) = max_theta l(theta)
                $$



                As written, it doesn't make sense.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered 9 hours ago









                Peter K.Peter K.

                1688




                1688




















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