On Fri, 07 Jun 2013 11:25:27 +0200, Cristiano <cristiapi@NSgmail.com> wrote:
>In this paper (275 kB): >https://wis.kuleuven.be/stat/robust/papers/2004/tailweightCOMPSTAT04.pdf >page 757 (page 5 of the pdf), there is the table 2 which is not clear >(to me). > >The column G_0,0.0 (which should mean N(0,1)) shows the JB statistics >for alpha= 5%. >For the cell JB / G_0,0.0 I expected to see something around 0.05 >instead of 0.038, because alpha= 0.05. >Please, could someone explain why there is 0.038?
The text says that this is the empirical result of 1000 random samples. Apparently, there were 38 "rejections" rather than 50, in this particular Monte Carlo experiment.
The 95% CI for 50 (as a Poisson, small count) is about (37, 65) so this result is not too unusual.
I do not notice whether they say that they use the exact same randomization for their other experiments. For the purpose of comparability -- since they do not perform enough trials to give a smaller CI -- it could have been wise to throw away samples of trials until they got one of, say, 47 or 53 (so the randomness is still very evident), and THEN to use exactly that same randomization for all trials. And to be up-front and clear to everyone, that this is what they did.
(but I won't study the article enough to see how much they actually do say.)