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From |
Maarten buis <maartenbuis@yahoo.co.uk> |

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 visiting address: Buitenveldertselaan 3 (Metropolitan), room Z434 +31 20 5986715 http://home.fsw.vu.nl/m.buis/ ----------------------------------------- __________________________________________________________ Sent from Yahoo! Mail. A Smarter Email http://uk.docs.yahoo.com/nowyoucan.html * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Difference between Monte Carlo simulation and the parametric bootstrap***From:*Richard Sperling <rsperling@rcn.com>

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