# Questions tagged [fisher-information]

For question about fisher information that appears in mathematical statistics.

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### Fisher Information for Beta Distribution when beta=1 [closed]

Let {X1, X2, . . . , Xn} is a random sample coming from Beta(α, β = 1), how can I calculate the Fisher Information I(α)?
1 vote
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### Intuition for vector calculus

In my statistics class, I was introduced to Fisher Information. As it comes from the Taylor Expansion in vector form, I wanted to know terms were ordered in a certain way - whether it was just to make ...
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### Computational Formula for Geodesic Distance on a Statistical Manifold

I am working on a problem where I need to compute the geodesic distance between two points on a statistical manifold. suppose we have two datasets $X$ and $Y$, I map them to PDF using the Kernel ...
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### Intuition of Wasserstein and Information geometry geodesics

Two important geometries that can be given to the space of multivariate Gaussian distributions are given by the Wasserstein distance and by the Fisher metric (ie. Information geometry). Although there'...
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1 vote
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### Asymptotic confidence interval using MLE and Fisher Information

We have observed x1, x2, ..., xn, independent samples from a Poisson distribution with an unknown mean λ > 0. Let $z_{1-α/2}$ denote the $1-\frac{α}{2}$ quantile of the standard normal distribution....
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### Tail bound version of Cramer-Rao

The Cramer-Rao bound is well-known: for an unbiased estimator $\hat{\theta}$, $$\text{var}(\hat\theta(X_1,...,X_n)) \geq\frac{1}{n}\mathcal{I}(\theta)^{-1}),$$ where $X_1,...,X_n\sim P_\theta$ i.i.d.,...
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1 vote
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### Construct a confidence interval for $\theta$

Let $X_{1}, \cdots, X_{n}$ be a random c.i.i.d sample such as, given $\theta$, $X_{1} \sim \mathcal{N}(0,\theta)$. Construct a confidence interval for $\theta$ using asymptotic results. This question ...
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