Statistics: Difference between revisions
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Use to test the ratio of variances. | Use to test the ratio of variances. | ||
===Likelihood Ratio Test=== | ===Likelihood Ratio Test=== | ||
See [[Wikipedia: Likelihood Ratio Test]]<br> | |||
* <math> LR = -2 \log \frac{\sup_{\theta \in \Theta_0} L(\theta)}{\sup_{\theta \in \Theta} L(\theta)}</math> | |||
===Uniformly Most Powerful Test=== | ===Uniformly Most Powerful Test=== | ||
UMP Test | UMP Test | ||
Revision as of 19:46, 16 December 2019
Statistics
Estimation
Maximum Likelihood Estimator
(MLE)
Uniformly Minimum Variance Unbiased Estimator
UMVUE, sometimes called MVUE or UMVU.
Tests
Basic Tests
T-test
Used to test the mean.
F-test
Use to test the ratio of variances.
Likelihood Ratio Test
See Wikipedia: Likelihood Ratio Test
- \(\displaystyle LR = -2 \log \frac{\sup_{\theta \in \Theta_0} L(\theta)}{\sup_{\theta \in \Theta} L(\theta)}\)
Uniformly Most Powerful Test
UMP Test
Anova
Confidence Sets
Confidence Intervals
Relationship with Tests
Regression
Quadratic Forms
Bootstrapping
Wikipedia
Boostrapping is used to sample from your sample to get a measure of accuracy of your statistics.
Nonparametric Bootstrapping
In nonparametric bootstrapping, you resample from your sample with replacement.
In this scenario, you don't need to know the family of distributions that your sample comes from.
Parametric Bootstrapping
In parametric bootstrapping, you learn the distribution parameters of your sample, e.g. with MLE.
Then you can generate samples from that distribution on a computer.