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Bootstrap; statistical assumptions. Rubin.

=====================Herman Rubin, 05 Nov 1995========sse Subject: Re: normal dist. (fwd) Message-ID: <47j0in$4av4@b.stat.purdue.edu> In article <DHG8K8.A6u@sun2.iusb.indiana.edu>, Frank Fujita <ffujita@sun1.iusb.edu> wrote: >Bob Hayden (hayden@oz.plymouth.edu) wrote: >: I guess I am automatically opposed to debating the REAL purpose of a >: list. One of my hopes for this one is that it will be a place where >: the many folks who are teaching statistics but are not extensively >: trained in it can learn more. >Well, that's me. But I think I disagree with you in that I'd say that >as soon as possible after teaching people the classical statistical >tests, we should not be teaching them how to look for deviations from >normality, but rather how to do a resampling test that doesn't have >any distributional assumptions. There are only a few procedures which have FEW distributional assumptions; all have SOME. The ones which have few are such things as the two-sample Kolmogorov-Smirnov test, and similar procedures; they require a continuous distribution. But why are people looking for deviations from normality? Much of the time, it makes little difference. And when it does, what is going to be done about it? There are estimation procedures which make use of an estimated distribution of the disturbances, but one can do relatively little in this direction without enormous sample sizes. >Are any of the knowledgable statisticians willing to give a critique of >the bootstrap and jack-knife techniques. The only discussion of them >that I've had is from proponents -- I like to hear from someone about >when the use of bootstrap and/or jack-knife techniques is inappropriate. One thing to keep in mind is that no procedure can get any information not in the sample. If there is a believed model, and there are is a low-dimensional sufficient statistic, there is no point in using an expensive procedure to try to get more. If one has a yes-no survey, then unless there is other information, no complicated procedure can get any information not in the sample size and the number of successes. Now what are these procedures claimed to do? The jackknife produces, under rather strong regularity conditions, more unbiased estimators. It does nothing else; the variance is not reduced. As most assessments of consequences emphasize the variance more than the bias, this is not of the greatest importance. Also, there are often cheaper and better ways to do this. The bootstrap is more complicated, but what it gets is presumably a better estimate of the precision of the estimator. I say presumably because the arguments involve large sample theory. Again, how important is this? At best, it can improve somewhat the calculation of classical significance levels or confidence intervals. The computer does not work magic. Even if the bootsrap gets a little more accuracy, is it worth it, and also, are we sure that we have not made additional assumptions to justify it? Usually, you can believe that the computer has done what it was told to. But the results are no better than the algorithm and programming behind them, and they are quite suspect here. -- * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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