How to compute variance/confidence intervals from Fisher information matrix. Mistake in this document?
$begingroup$
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:
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
edited Dec 22 '18 at 18:19
Martijn Weterings
12.7k1457
asked Dec 22 '18 at 16:44
OthewOthew
211
$endgroup$
add a comment |
$begingroup$
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:
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
edited Dec 22 '18 at 18:19
Martijn Weterings
12.7k1457
asked Dec 22 '18 at 16:44
OthewOthew
211
$endgroup$
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
add a comment |
$begingroup$
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:
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
edited Dec 22 '18 at 18:19
Martijn Weterings
12.7k1457
asked Dec 22 '18 at 16:44
OthewOthew
211
$endgroup$
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:
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
edited Dec 22 '18 at 18:19
Martijn Weterings
12.7k1457
asked Dec 22 '18 at 16:44
OthewOthew
211
edited Dec 22 '18 at 18:19
Martijn Weterings
12.7k1457
asked Dec 22 '18 at 16:44
OthewOthew
211
edited Dec 22 '18 at 18:19
Martijn Weterings
12.7k1457
edited Dec 22 '18 at 18:19
Martijn Weterings
12.7k1457
edited Dec 22 '18 at 18:19
Martijn Weterings
12.7k1457
12.7k1457
asked Dec 22 '18 at 16:44
OthewOthew
211
asked Dec 22 '18 at 16:44
OthewOthew
211
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
add a comment |
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
add a comment |
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 $$Var (hattheta) approx frac{1}{I_n(theta)} = frac{1}{n I_1 (theta)}$$
answered Dec 22 '18 at 17:13
Martijn WeteringsMartijn Weterings
12.7k1457
$endgroup$
add a comment |
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$begingroup$
See section 1.4 about the confusion between $I_n(theta)$ and $I_1(theta)$.
You have $$Var (hattheta) approx frac{1}{I_n(theta)} = frac{1}{n I_1 (theta)}$$
answered Dec 22 '18 at 17:13
Martijn WeteringsMartijn Weterings
12.7k1457
$endgroup$
add a comment |
$begingroup$
See section 1.4 about the confusion between $I_n(theta)$ and $I_1(theta)$.
You have $$Var (hattheta) approx frac{1}{I_n(theta)} = frac{1}{n I_1 (theta)}$$
answered Dec 22 '18 at 17:13
Martijn WeteringsMartijn Weterings
12.7k1457
$endgroup$
add a comment |
$begingroup$
See section 1.4 about the confusion between $I_n(theta)$ and $I_1(theta)$.
You have $$Var (hattheta) approx frac{1}{I_n(theta)} = frac{1}{n I_1 (theta)}$$
answered Dec 22 '18 at 17:13
Martijn WeteringsMartijn Weterings
12.7k1457
$endgroup$
See section 1.4 about the confusion between $I_n(theta)$ and $I_1(theta)$.
You have $$Var (hattheta) approx frac{1}{I_n(theta)} = frac{1}{n I_1 (theta)}$$
answered Dec 22 '18 at 17:13
Martijn WeteringsMartijn Weterings
12.7k1457
edited Dec 22 '18 at 17:19
answered Dec 22 '18 at 17:13
Martijn WeteringsMartijn Weterings
12.7k1457
answered Dec 22 '18 at 17:13
Martijn WeteringsMartijn Weterings
12.7k1457
answered Dec 22 '18 at 17:13
Martijn WeteringsMartijn Weterings
12.7k1457
12.7k1457
add a comment |
add a comment |
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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