Greg wrote: > I want to use the bootstrap to test H0: g(x) = 0 vs Ha: g(x) > 0, > where g() is a very coplicated non-negative function of the data. > Using a one-sided percentile (nonparametric) confidence interval seems > very easy, i.e. for an alpha = 0.05 test, reject H0 if g-hat > the > 95th percentile of the bootstrap distribution of g. > > My question is, am I overlooking any problems or subtleties stemming > from the fact the g is strictly non-negative? > > Thanks, > Greg
Yes, and possibly overlooking all the subtleties of bootstrapping itself. There are many approachs within boostrapping and I don't claim to be familiar with them all, but one of them would be as follows for the problem you describe. The "bootstrap distribution" used in the test should be derived from a version of the data adapted so that the null hypothesis is exactly true ...thus if you were testing for a mean of zero, you would foramlly base the bootstrap distribution on a data set adjusted to have a mean of zero, usually by subtracting the sample mean although other things are possible. In your case you would need to find an adjustment of the data so that g(x)=0 does hold. Can you do this? Here the interpretation of this condition probably becomes important. I think what you need is for the "population value" of "g(x)" to be zero, where the adjusted data sample is treated as the whole population. Unless you do some sort of adjustment, what you will tend to get is (apart from some possible slight bias effects) a distribution which is always centred on your sample value. David Jones . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
