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Parametric Bootstrap vs. Nonparametric Bootstrap

Sep 10th, 2008| 10:46 pm | Posted by hlee

The following footnotes are from one of Prof. Babu’s slides but I do not recall which occasion he presented the content.

– In the XSPEC packages, the parametric bootstrap is command FAKEIT, which makes Monte Carlo simulation of specified spectral model.
– XSPEC does not provide a nonparametric bootstrap capability.


Parametric Bootstrap: X_1^*,...,X_n^* \sim F(\cdot;\theta_n)
Both \sqrt{n} \sup_x |F_n(x)-F(x;\theta_n)| and \sqrt{n} \sup_x |F_n^*(x)-F(x;\theta_n^*)| have the same limiting distribution.[1]

Nonparametric Bootstrap:X_1^*,...,X_n^* \sim F_n.
A bias correction B_n(x)=F_n(x)-F(x;\theta_n) is needed.
\sqrt{n} \sup_x |F_n(x)-F(x;\theta_n)| and \sqrt{n} \sup_x |F_n^*(x)-F(x;\theta_n^*)-B_n(x)| have the same limiting distribution.[2]

  1. In the XSPEC packages, the parametric bootstrap is command FAKEIT, which makes Monte Carlo simulation of specified spectral model.[↩]
  2. XSPEC does not provide a nonparametric bootstrap capability[↩]
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