Through an example: what is parametric and non-parametric boostrap? 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?
 A: 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.
