All Questions
Tagged with fisher-information hypothesis-testing
8
questions
6
votes
4
answers
590
views
What is the information in an exact p-value?
Consider the following two statistical principles: 1) an exact test's $p$-value gives the exact frequency with which the observed random sample appears by chance, i.e., under a true null hypothesis; ...
- 642
1
vote
1
answer
28
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Why does the score test work for values longer in the tail that have a small log-likelihood derivative?
The score test says that we take the derivative of the log-likelihood at $H_0$ and divide it by the fisher information at $H_0$.
$U(\theta )={\frac {\partial \log L(\theta \mid x)}{\partial \theta }}.$...
0
votes
0
answers
61
views
Fiding the test statistic, using wald test
Given the random sample $X_1,...,X_n \sim N(\mu, \sigma^2)$, I want to perform a Wald test for:
$\mathrm{H}_\mathrm{0}: \mu = \mathrm{\mu}_\mathrm{0}$
$\mathrm{H}_\mathrm{1}: \mu \neq \mathrm{\mu}_\...
- 543
6
votes
2
answers
737
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Is it true that we can always increase statistical power/estimator precision by increasing sample size?
Suppose a test has ~$16.67\%$ power to detect some arbitrary but fixed effect size when sample size is $3$, and as we increase size by adding IID random observations to the sample ${4, 5, 6, 7,...}$ ...
- 642
5
votes
2
answers
2k
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Statistical comparison of (covariance) matrices
I am trying to test whether the covariance matrix for the maximum likelihood estimates for a gaussian general linear model approaches the inverse Fisher information matrix (times 1/n , n being the ...
- 173
0
votes
0
answers
28
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Does Fisher Information quantify precision? [duplicate]
Looking at perspective from estimating the actual value from a set of data measured by the instrument. Does Fisher information just quantify the precision of the measurement?
What does it say about ...
- 101
1
vote
1
answer
601
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Different version of Wald test statistic formula
I came across two formulas for the Wald test statistic in a maximum likelihood framework:
One has $(R\hat{\theta}-r)'(RI_n^{-1}R')^{-1}(R\hat{\theta}-r)$, where $I_n^{-1}$ is the inverse of the ...
- 11
2
votes
0
answers
2k
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wald test and score test, normal or chi square?
I learnt from section 10.3 of statistical inference that both Wald test statistic $\frac{W_n-\theta_0}{S_n}\approx\frac{W_n-\theta_0}{\sqrt{\hat I_n(W_n)}}$ and score test statistic $\frac{S(\theta_0)}...
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