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From |
Stas Kolenikov <skolenik@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: bootstrap test, combined bootstrap datasets, statistical properties of the bootstrap |

Date |
Tue, 4 May 2010 09:11:16 -0500 |

On Tue, May 4, 2010 at 3:43 AM, Gianluca Cafiso <gcafiso@unict.it> wrote: > My doubt is the following: > Is the test based on the unique dataset (as generated at point 3) still > valid? Or, for the so-generated dataset, do the usual distributional > properties -on which Bootstrap-based tests are based- not hold? Which exactly properties are you worried about? I am sure one can construct a valid bootstrap scheme for your situation. I would be more worried about other issues, however. 1. It looks like you are dealing with time series. If that's the case, you are dealing with dependent data, and you have to use some sort of blocking schemes. 2. If that's indeed time series, and the two series overlap, then you should ask yourself a question, "Do I want to try and resample the same periods in both series?" If the series are cross-correlated, you'd have to do that. 3. Using the bootstrap for hypothesis testing is quite complicated. To get the bootstrap distribution of the test statistic, you have to sample from a distribution in which the null is satisfied. Your setup is very odd in this respect: you don't have a point null, and you don't even have the null that contains the boundary point (as the worst case null), so I cannot even conceptually think of a test that could work in your case. If you really have an open interval for your null, then asymptotically all probabilities are either 0 or 1, so cannot construct an asymptotic test that would have an intermediate size like 5%. In other situations, there are ways to get the bootstrap p-value of some reasonable tests. But to get there, you need to transform your data so that the null is satisfied. In testing the mean, you'd need to shift your data; in multivariate analysis, you need to rotate them; in time series, you probably need to filter them somehow (even though that might kill the very effect you are trying to test). If you do the bootstrap with the raw data, you can only get a confidence interval of a kind for the observed value of your statistic, but that'll be it. You cannot get the null distribution of the test statistic or a p-value unless you resample under the null. -- Stas Kolenikov, also found at http://stas.kolenikov.name Small print: I use this email account for mailing lists only. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: bootstrap test, combined bootstrap datasets, statistical properties of the bootstrap***From:*Gianluca Cafiso <gcafiso@unict.it>

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