# Questions tagged [fisher-information]

The Fisher information measures the curvature of the log-likelihood and can be used to assess the efficiency of estimators.

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### Should one account for the known variance of fixed X when estimating its relationship with random Y?

In Aldrich (2005), and specifically in sections 10 and 11, the author describes the sufficient statistic for the parameter $\beta$ in the simple regression of random $Y$ on fixed $X$, with a bivariate ...
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### Confusion over Fisher-scoring algorithm

Given a probability model $f(X;\theta)$ and a set of i.i.d. observations $x_1,\ldots,x_n$ which we assume to be drawn from some true parameter $f(X; \theta_0)$, we can perform maximum-likelihood ...
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### Derivative of the Score Function in Fisher Information

I'm studying Fisher Information and am trying to develop an intuitive understanding. Keep in mind I only have bachelor level mathematics background so I would appreciate an answer that is more ...
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1 vote
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### Expected value of derivative derivative squared log equivalent to regularity condition

I'm given the following information (*): $\mathbb E[(\frac{\partial}{\partial \theta} log f(X_1, ..., X_n; \theta))^2] = - \mathbb E[(\frac{\partial^2}{\partial^2 \theta} log f(X_1, ..., X_n; \theta))$...
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1 vote
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### Why can we get better asymptotic global estimators even for IID random variables?

Let $X_1,...,X_N$ be IID random variables sampled from a parametrised distribution $p_\theta$, and suppose my goal is to retrieve $\theta$ from these samples. We know that the MLE provides an ...
• 383
1 vote
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### How does reparametrization of the Fisher information matrix change the variance expression for the sufficient statistics?

If I have an exponential family distribution of the form $$p_{\theta}(x) = e^{\theta^T\cdot t(x) - \psi(\theta)},$$ where $\theta$ is a vector of parameters, $t(x)$ is a vector of sufficient ...
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### Bootstrap method with 2 Fisher matrices in order to do the cross-correlations between both

I have 2 Fisher matrices where each colum/row represents the information (in Fisher's sense) of astrophysical parameters. These parameters are in the same order for both matrices. Now, I would like to ...
1 vote
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