187 views

### Interpretation of the elements of the error matrix as inverse of hessian matrix [duplicate]

In a report I am reading at work, the error matrix is calculated as the inverse of the hessian matrix and used to calculate the error ellipse angle and axes with a not theoretically correct formula. ...
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1 vote
30 views

### How do I construct a variance-covariance matrix from a matrix formulation of a MLR? [duplicate]

I'm trying to calculate the SE for each coefficient given by a matrix formulation of MLR by the root of each diagonal in the so-called variance-covariance matrix, but I'm unsure how to construct this ...
19k views

### Relationship between Hessian Matrix and Covariance Matrix

While I am studying Maximum Likelihood Estimation, to do inference in Maximum Likelihood Estimaion, we need to know the variance. To find out the variance, I need to know the Cramer's Rao Lower Bound, ...
• 1,673
9k views

### Why is the Fisher information the inverse of the (asymptotic) covariance, and vice versa?

For the multinomial distribution, I had spent a lot of time and effort calculating the inverse of the Fisher information (for a single trial) using things like the Sherman-Morrison formula. But ...
• 6,169
8k views

### How to estimate confidence interval of a least-squares fit parameters by means of numerical Jacobian

I am working on a complicated data fitting algorithm in Matlab. I have a problem with properly estimating the confidence intervals of my fit. I will describe my procedure in some detail, give some of ...
5k views

### How to compute (or numerically estimate) the standard error of the MLE

I have a model for which I know the log likelihood function, the gradient of the log likelihood and the Hessian of the log likelihood. For given data I can compute the MLE using a generic optimizer (...
• 2,019
4k views

### Fisher information from MLE in R?

Reworded the question: I have read "The Fisher information I(p) is this negative second derivative of the log-likelihood function, averaged over all possible X = {h, N–h}, when we assume some value ...
3k views

### Why need wald test ( a squared version of t test ) when we already have t test?

It seems to me that they are basically calculate the same thing. Since we already have t-test, why do we need a squared version (wald test)? Does wald test have its own advantage? For example in Cox ...
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2k views

### Wald test standard error

I want to compute from scratch a Wald test to test significance of one coefficient in a logistic regression model. I've been to so many posts and blogs but couldn't find a clear explanation with ...
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2k views

### How does coxph calculate standard errors?

How are the standard errors in the coxph function in R calculated? According to Fox, "The column marked z in the output records the ratio of each regression coefficient to its standard error, a Wald ...
• 519
2k views

### Expected and observed Fisher information? [duplicate]

Studying asymptotics, I bumped into the concept of Observed Fisher Information, as a way to compute Fisher Information when the parameter $\theta$ is unknown. I am also aware that it is related in ...
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2k views

### Negative Hessian matrix in R optim [closed]

I used the optim() function in R to find the min log likelihood, however the diagonal elements of the inverse of Hessian matrix turned out to be negative. ...
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1 vote
350 views

### Fisher information vs Posterior Covariance

I have a parameter $\theta$ and data $y = f(\theta) + \mathrm{noise}$. My goal is finding the best fit for $\theta$ and assess the uncertainty I have on this best fit. I see two competing approaches ...
• 73
1 vote
701 views

### Observed Fisher Information and confidence intervals

I'm trying to put confidence intervals on parameters fitted through MLE through the inversion of the observed Fisher information matrix. More specifically, I define the observed FIM as:  J_{n}(\hat{...
1 vote