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.
