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I cannot believe how abstractly some sources explain this, practically not explaining it at all.

So what's parametric and non-parametric bootstrap and how are they different?

mavavilj
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  • You can view a nice tutorial here: http://www.stat.umn.edu/geyer/5601/examp/parm.html – StatsStudent Mar 03 '16 at 19:58
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    The distinction might be that the non-parametric bootstrap makes no assumptions about the distribution of the observed data, but merely calculates statistics directly from samples taken from the data. The parametric bootstrap assumes the observations follow a distribution and estimates the parameters for that distribution, then draws samples from the chosen distribution (with the estimated parameter, e.g. $\theta$) and calculates statistics. Both are used to calculate same sorts of statistics. – mavavilj Mar 03 '16 at 20:43

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I'll give you an example. Let's say you have the data set $x_1,\dots,x_n$, which you think comes from the normal distribution.

In parametric bootstrapping, you estimate the parameters of normal distribution $\hat\mu,\hat\sigma$, then you generate new sample from $x_1^*,\dots,x^*_n\sim\mathcal{N}(\hat\mu,\hat\sigma^2)$

You can generate as many samples $x_1^*,\dots,x^*_n$ as needed for you Monte Carlo simulation.

In non-parametric bootstrapping, you build empirical distribution function (EDF), then generate the sample $x_1^*,\dots,x^*_n$ directly from EDF, not from the estimated normal distribution as in parametric bootstrapping.

It happens so that in some applications non-parametric bootstrapping leads to biased estimation, while parametric is unbiased, e.g. see G. Jogesh Babu, Eric D. Feigelson, "Astrostatistics: Goodness-of-Fit and All That!", in Astronomical Data Analysis Software and Systems XV, ASP Conference Series, Vol. 351, 2006. The paper is about K-S test critical values estimation.

Aksakal
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  • I read that there can be parametric bootstrap with empirical CDF. – mavavilj Mar 03 '16 at 20:31
  • There's no way to explain everything by examples, that's why you have abstract descriptions: to capture the general case. If you have a particular concern, you should bring it up. – Aksakal Mar 03 '16 at 20:36
  • I'm just saying that the empirical CDF cannot be the distuinguishing feature if both parametric and non-parametric can utilize it. – mavavilj Mar 03 '16 at 20:37
  • Can you show an example? – Aksakal Mar 03 '16 at 20:40
  • No, because it's an observation from my lecture notes, which I won't share. – mavavilj Mar 03 '16 at 20:41
  • How is parametric bootstrap different from a Monte Carlo simulation? – Macond Apr 20 '17 at 14:49
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    @Macond, bootstrapping is a kind of Monte Carlo simulation. Maybe not every kind of bootstrapping, but certainly those that I came across are – Aksakal Apr 20 '17 at 15:43