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Re: st: RE: Kolmogorov-Smirnov test for the first order stochastic dominance


From   "Stas Kolenikov" <skolenik@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: Kolmogorov-Smirnov test for the first order stochastic dominance
Date   Tue, 5 Sep 2006 09:32:18 -0500

In the output of -ksmirnov-, you would see the two one-sided
statistics, with the final one being the max of them. So I would guess
it would be easy to check the stochastic dominance of one empirical
distribution vs. the other -- just to look whether one of the
distances is identically zero. What is probably far more difficult is
to test whether the two population distributions have the stochastic
dominance, based on the samples from the two. I vaguely remember
Russell Davidson was doing some work on that a few years back for some
inequality and poverty comparisons, but I lost track of that
literature, unfortunately :((.

You might also want to check references on order restricted inference.
There was a major book published in the late 1980s with that title,
but I don't know whether it deals with your situation directly.

On 9/4/06, Nick Cox <n.j.cox@durham.ac.uk> wrote:
If -findit- using these keywords produced nothing,
the answer is that you need to program it yourself,
use some other software or consider another technque.

Stata people tend not to be too keen on these little
tests from the past. There is more information in a
quantile-quantile plot.

Nick
n.j.cox@durham.ac.uk

Chiara

> I need to perform the non -parametric Kolmogorov-Smirnov test for
> first-order stochastic
> dominance of one distributions over another. How can I do it in Stata?
>  The *ksmirnov* command in Stata performs only
> Kolmogorov-Smirnov tests
> of the equality of distributions but I also need to determine
> whether or
> not a distribution dominates the other.


--
Stas Kolenikov
http://stas.kolenikov.name
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