Restrictive first order stochastic dominance, Davidson and Duclos (2009)

[Spirae Raïs]

Dear all,
I am currently working on a project where I am comparing the distribution of clinical trials across two groups of pathologies A and B. I'll write Fa(Clinical trials) to designate "the distribution of clinical trials for diseases in group A", same for B.
I would like to use first-order stochastic dominance and test the null hypothesis of non-dominance of Fa(Clinical trials) over Fb(Clinical trials), against the alternative hypothesis that Fa(Clinical trials) first-order stochastically dominates Fb(Clinical trials).
This was done in Dirk Van de gaer Joost Vandenbossche José Luis Figueroa (2014), here is the working paper: http://documents.worldbank.org/curat...df/wps6345.pdf
Guidance is coming from Davidson and Duclos (2009): https://halshs.archives-ouvertes.fr/...43560/document
Is there any user-written program for this procedure (I found ksmirnov, but the null hypothesis is dominance)? If not, can you give me a little bit of guidance on how to conduct the tests I am interested in?

Thank you very much for your time and help with my question,
Please don't hesitate if you need further detail

All the best,
Spirae

[David Kaplan]

You can use the distcomp command. See
https://faculty.missouri.edu/kapland....html#distcomp
for links to the Stata Journal article and instructions for installation (or run net from http://faculty.missouri.edu/kaplandm and click "distcomp" to read more and install).
The reported "rejected ranges" are the ranges over which there is restricted first-order stochastic dominance (RSD1).

Some (important) technical details:
0. I think this was just a typo in your post, but to clarify (esp. for other readers), the alternative is restricted first-order stochastic dominance; as explained by Davidson and Duclos (p. 87 of the published 2013 version), "The article also shows that it is not possible with continuous distributions to reject nondominance in favor of dominance over the entire supports of the distributions."
1. The distcomp reported results are actually two-sided, so
a) double-check the direction of dominance in the generated plot (that shows the ECDFs along with the rejected ranges)
b) divide the significance level by two (e.g., if you use "10%" reported results, call them 5% if you're discussing restricted dominance) (technically it's 5.1%...1-sqrt(1-0.1)=0.051)
2. The reported ranges are "conservative" in the following senses.
a) "confidence" interpretation: there is high probability (e.g., 95%) that the reported ranges are a subset of the true ranges of values over which there is RSD1.
b) "multiple testing" interpretation: falsely rejecting non-dominance in favor of dominance at even one single point (i.e., including that point in the "rejected ranges") has a low probability (e.g., 5%).
3. Unlike Davidson and Duclos, you don't need to pre-specify the range for RSD1 and then test only that range; distcomp determines the range automatically. Also, instead of their empirical likelihood bootstrap, distcomp uses other methodology that yields exact finite-sample error rates and helps distribute power evenly across the distribution; details are in a Journal of Econometrics paper (and partly in the Stata Journal article) linked here (both published and not-quite-published versions):
https://faculty.missouri.edu/kapland...x.html#distinf

[David Kaplan]

Updated links/command for my prior post (university shut down our web server...):
- https://kaplandm.github.io/#distcomp
- net from https://kaplandm.github.io/stata
- https://kaplandm.github.io/#distinf