## Bootstrap

### Bootstrap

Bootstrapping is a statistical method for estimating the sampling distribution of an estimator by sampling with replacement from the original sample, most often with the purpose of deriving robust estimates of standard errors and confidence intervals of a population parameter like a mean, median, proportion, odds ratio, correlation coefficient or regression coefficient. It may also be used for constructing hypothesis tests. It is often used as a robust alternative to inference based on parametric assumptions when those assumptions are in doubt, or where parametric inference is impossible or requires very complicated formulas for the calculation of standard errors.

The Bootstrap method is a technique for making inferences about a population’s characteristics. It is a computer intensive statistical method that uses simulation to estimate standard errors, construct confidence intervals and carryout significance testing based not on assumptions of normality but on empirical resampling with replacement of the data. Taking a large number of random samples from the dataset generates information on the variability of parameter estimates, and the larger the sample, the more the precision of bootstrapped error estimates.

Efron invented the name”boostrap” from and old saying about “pulling yourself up by your owb bootstrap” . it reflects the idea that one available sample give rise to many others.

**Non parametric Bootstrap **

This method relies on the fact that the empirical distribution function based on the sample is an estimate of the distribution of the population; in this wise, it is very imperative that this sample should be a true representative of the population. It resample randomly with replacement from the original data.

**Parametric Bootstrap**

The parametric bootstrap is based on parametric assumptions. We assume that the response variable has a specific distribution.

**Semi Parametric Bootstrap**

The semi parametric method is based on the bootstrap the residuals, also called residual bootstrap. The main idea is to resample from an empirical version of the error distribution.