Re: st: Using Wilcoxon rank-sum (Mann-Whitney) test to compare an emipirical and a uniform distribution

["JVerkuilen (Gmail)" <jvverkuilen@gmail.com>]

On Sat, Mar 9, 2013 at 8:49 AM, Tsankova, Teodora <TsankovT@ebrd.com> wrote:
> Dear David,
>
> Thank you for the suggestion.
>
> What I mean is that I create a uniform distribution between 0 and 1 with
> 15 observation. Given that every value should have the same probability
> under a uniform distribution I divide 1 by 14 and create those equally
> spaces 15 values. Plotting the CDF of those values would result in a
> straight diagonal line which is ultimately what the ksmirnov test would
> test against as well.
>

So it looks from ksmirnov that you reject the null of uniformity but,
naturally enough, want some measure of directionality. That's why I
think many of us were dubious of ksmirnov in the first place. However,
you can invert it to generate a confidence interval by working out
what the rejection region of the relevant test is and plotting it
using quantile. I don't have access to a book on nonparametric
statistics (such as Gibbons & Chakraborti) at the moment, but I've
done this to generate a confidence interval for the ECDF. However, the
resulting confidence interval is usually very wide. In the past when I
had this problem I seem to recall bootstrapping worked out better. (It
was a long time ago, I'm not sure I recall how.)

Gibbons, J. D., and S. Chakraborti. 2011. Nonparametric Statistical
Inference. 5th ed. Boca Raton, FL: Chapman & Hall/CRC.


-- 
JVVerkuilen, PhD
jvverkuilen@gmail.com

"It is like a finger pointing away to the moon. Do not concentrate on
the finger or you will miss all that heavenly glory." --Bruce Lee,
Enter the Dragon (1973)
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