# Re: st: Difference between Monte Carlo simulation and the parametric bootstrap

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: Difference between Monte Carlo simulation and the parametric bootstrap Date Mon, 23 Jun 2008 19:12:58 +0100 (BST)

```--- Richard Sperling <rsperling@rcn.com> wrote:
> I would appreciate it if someone could clarify the distinction
> between Monte Carlo simulation and the parametric bootstrap. If I'm
> not mistaken, one use of Monte Carlo simulation is to assess the
> sampling distribution of an estimator. In contrast, the parametric
> bootstrap is used to estimate the variance of a statistic and its
> sampling distribution.
>
> But don't both the Monte Carlo method and parametric bootstrap
> require specifying a data generating process? It is at this point
> where I'm a little confused and fail to see the distinction between
> the two methods.
>
> Also note that I am not talking about the non-parametric bootstrap.

In principle both the parametric and the non-parametric bootstrap are
special cases of Monte Carlo simulations used for a very specific
purpose: estimate some characteristics of the sampling distribution.
Remember that the sampling distribution of statistic could be obtained
if we could draw many samples from the population and compute a
statistic in each sample. The idea behind the bootstrap is that the
sample is an estimate of the population, so an estimate of the sampling
distribution can be obtained by drawing many samples (with replacement)
from the observed sample, compute the statistic in each new sample. In
case of the parametric bootstrap you add some extra restrictions while
sampling from the data, but that does not change the point here.

Monte Carlo simulations are more general: basically it refers to
repeatedly creating random data in some way, do something to that
random data, and collect some results. This strategy could be used to
estimate some quantity, like in the bootstrap, but also to
theoretically investigate some general characteristic of an estimator
which is hard to derive analytically.

In practice it would be pretty safe to presume that whenever someone
speaks of a Monte Carlo simulation they are talking about a theoretical
investigation, e.g. creating random data with no empirical content what
so ever to investigate whether an estimator can recover known
characteristics of this random `data', while the (parametric) bootstrap
refers to an emprical estimation. The fact that the parametric
bootstrap implies a model should not worry you: any empirical estimate
is based on a model.

Hope this helps,
Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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