> ... Simple consideration of the balancing > shows that this level should decrease with increasing sample size. > In low dimensional problems, with the cost of incorrect acceptance > going as the k-th power of the error, the rate at which the level > decreases should be about 1/n^((d+k/2).
Dear Professor Rubin (or anyone else capable of answering),
I would be really grateful if you could explain that paragraph to a broader audience, i.e., to mathematically challenged applied statisticians like me.
I gues "incorrect acceptance" means "incorrect acceptance of the null hypothesis", i.e., type II error? Secondly, a bracket is missing in the power to which n should be raised -- should is come after k? Thirdly, would k be chosen in the sense of 2 for "quadratic loss" (like, e.g., in the <Taguchi world>)? And Fouthly and most puzzlingly (at least to me), what does d stand for?
It would be great if you could also add a simple example (sample calculation).
I have to admit that I might eventually use this in a "statistically eclectic" real-life application. (It's about combining traditional SPC/SQC/control charts with some more enlightened inference and visualisation, like it's become something of a trend in health care quality research and monitoring in Europe, especially in the UK -- if interested, see the works of Spigelhalter in several top-notch statistical and medical journals; I've also published one article on it in a less prestigeous stats journal). So I realise it's basically against your principles/commandmends, but nevertheless, I hope you're willing to do me this favour.
Best regards, Assist Prof Gaj Vidmar Univ. Ljubljana, Fac. Medicine, Inst. Biostatistics & Med. Inf.