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Topic: simple question
Replies: 11   Last Post: Jul 6, 2012 3:54 PM

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Gaj Vidmar

Posts: 21
Registered: 12/13/04
Re: simple question
Posted: Jul 6, 2012 9:27 AM
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> ... 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.

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