# Statistics

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Statistics

## Contents

## 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

### 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.