How to compute variance/confidence intervals from Fisher information matrix. Mistake in this document?












1












$begingroup$


https://www.stat.umn.edu/geyer/5931/mle/mle.pdf



In this document (by the great Geyer nonetheless!)



it calculates confidence intervals using the Fisher matrix:



enter image description here



But the standard deviation is not the square-root of the element in the fisher matrix, you have to divide by $n$ first! Is this a huge mistake?






confidence-interval fisher-information







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    How does nlm compute Hessians? is it possible that the factor is already absorbed into inv.fish?
    $endgroup$
    – Demetri Pananos
    Dec 22 '18 at 16:52










  • $begingroup$
    Why would it do that? If I want to compute the hessian, surely it ought to give me the hessian, otherwise what's the point?
    $endgroup$
    – Othew
    Dec 22 '18 at 16:57










  • $begingroup$
    We need an expert in here!
    $endgroup$
    – Othew
    Dec 22 '18 at 16:58
















1












$begingroup$


https://www.stat.umn.edu/geyer/5931/mle/mle.pdf



In this document (by the great Geyer nonetheless!)



it calculates confidence intervals using the Fisher matrix:



enter image description here



But the standard deviation is not the square-root of the element in the fisher matrix, you have to divide by $n$ first! Is this a huge mistake?






confidence-interval fisher-information







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    How does nlm compute Hessians? is it possible that the factor is already absorbed into inv.fish?
    $endgroup$
    – Demetri Pananos
    Dec 22 '18 at 16:52










  • $begingroup$
    Why would it do that? If I want to compute the hessian, surely it ought to give me the hessian, otherwise what's the point?
    $endgroup$
    – Othew
    Dec 22 '18 at 16:57










  • $begingroup$
    We need an expert in here!
    $endgroup$
    – Othew
    Dec 22 '18 at 16:58














1












1








1





$begingroup$


https://www.stat.umn.edu/geyer/5931/mle/mle.pdf



In this document (by the great Geyer nonetheless!)



it calculates confidence intervals using the Fisher matrix:



enter image description here



But the standard deviation is not the square-root of the element in the fisher matrix, you have to divide by $n$ first! Is this a huge mistake?






confidence-interval fisher-information







share|cite|improve this question











$endgroup$




https://www.stat.umn.edu/geyer/5931/mle/mle.pdf



In this document (by the great Geyer nonetheless!)



it calculates confidence intervals using the Fisher matrix:



enter image description here



But the standard deviation is not the square-root of the element in the fisher matrix, you have to divide by $n$ first! Is this a huge mistake?






confidence-interval fisher-information




confidence-interval fisher-information






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 22 '18 at 18:19









Martijn Weterings

12.7k1457




12.7k1457










asked Dec 22 '18 at 16:44









OthewOthew

211




211








  • 1




    $begingroup$
    How does nlm compute Hessians? is it possible that the factor is already absorbed into inv.fish?
    $endgroup$
    – Demetri Pananos
    Dec 22 '18 at 16:52










  • $begingroup$
    Why would it do that? If I want to compute the hessian, surely it ought to give me the hessian, otherwise what's the point?
    $endgroup$
    – Othew
    Dec 22 '18 at 16:57










  • $begingroup$
    We need an expert in here!
    $endgroup$
    – Othew
    Dec 22 '18 at 16:58














  • 1




    $begingroup$
    How does nlm compute Hessians? is it possible that the factor is already absorbed into inv.fish?
    $endgroup$
    – Demetri Pananos
    Dec 22 '18 at 16:52










  • $begingroup$
    Why would it do that? If I want to compute the hessian, surely it ought to give me the hessian, otherwise what's the point?
    $endgroup$
    – Othew
    Dec 22 '18 at 16:57










  • $begingroup$
    We need an expert in here!
    $endgroup$
    – Othew
    Dec 22 '18 at 16:58








1




1




$begingroup$
How does nlm compute Hessians? is it possible that the factor is already absorbed into inv.fish?
$endgroup$
– Demetri Pananos
Dec 22 '18 at 16:52




$begingroup$
How does nlm compute Hessians? is it possible that the factor is already absorbed into inv.fish?
$endgroup$
– Demetri Pananos
Dec 22 '18 at 16:52












$begingroup$
Why would it do that? If I want to compute the hessian, surely it ought to give me the hessian, otherwise what's the point?
$endgroup$
– Othew
Dec 22 '18 at 16:57




$begingroup$
Why would it do that? If I want to compute the hessian, surely it ought to give me the hessian, otherwise what's the point?
$endgroup$
– Othew
Dec 22 '18 at 16:57












$begingroup$
We need an expert in here!
$endgroup$
– Othew
Dec 22 '18 at 16:58




$begingroup$
We need an expert in here!
$endgroup$
– Othew
Dec 22 '18 at 16:58










1 Answer
1






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$begingroup$

See section 1.4 about the confusion between $I_n(theta)$ and $I_1(theta)$.



You have $$Var (hattheta) approx frac{1}{I_n(theta)} = frac{1}{n I_1 (theta)}$$






share|cite|improve this answer











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    1 Answer
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    active

    oldest

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    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    5












    $begingroup$

    See section 1.4 about the confusion between $I_n(theta)$ and $I_1(theta)$.



    You have $$Var (hattheta) approx frac{1}{I_n(theta)} = frac{1}{n I_1 (theta)}$$






    share|cite|improve this answer











    $endgroup$


















      5












      $begingroup$

      See section 1.4 about the confusion between $I_n(theta)$ and $I_1(theta)$.



      You have $$Var (hattheta) approx frac{1}{I_n(theta)} = frac{1}{n I_1 (theta)}$$






      share|cite|improve this answer











      $endgroup$
















        5












        5








        5





        $begingroup$

        See section 1.4 about the confusion between $I_n(theta)$ and $I_1(theta)$.



        You have $$Var (hattheta) approx frac{1}{I_n(theta)} = frac{1}{n I_1 (theta)}$$






        share|cite|improve this answer











        $endgroup$



        See section 1.4 about the confusion between $I_n(theta)$ and $I_1(theta)$.



        You have $$Var (hattheta) approx frac{1}{I_n(theta)} = frac{1}{n I_1 (theta)}$$







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Dec 22 '18 at 17:19

























        answered Dec 22 '18 at 17:13









        Martijn WeteringsMartijn Weterings

        12.7k1457




        12.7k1457






























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