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st: -bkrosenblatt- available from SSC


From   n j cox <n.j.cox@durham.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   st: -bkrosenblatt- available from SSC
Date   Wed, 17 Oct 2007 20:21:08 +0100

Thanks to the ever-active Kit Baum, a new package -bkrosenblatt-
is available from SSC. Stata 9.2 is required. Use -ssc- in the
usual way to install, whether or not you are interested.

-bkrosenblatt- implements a test due to Blum, Kiefer and Rosenblatt
(1961) of bivariate independence, itself a variant on a test
due to Hoeffding (1948). (Full references are given in the
detailed help, which includes Stata manual-style vignettes on
Blum, Kiefer, (Murray) Rosenblatt and Hoeffding.) I am agnostic
about how useful this test really is, but it was fun to program,
and when a biostatistician of the standing of Frank Harrell
says that the Hoeffding test is useful, as he does in his
monograph _Regression modeling strategies_ (New York,
Springer 2001), then data analysts should pay attention.

So why does the program implement the Blum, Kiefer and Rosenblatt
test, rather than the Hoeffding test? The usual rummaging around
identified two useful recent papers

Mudholkar, G.S. and Wilding, G.E. 2003.  On the conventional wisdom
regarding two consistent tests of bivariate dependence.  The
Statistician 52: 41-57.

Mudholkar, G.S. and Wilding, G.E. 2005.  Two Wilson-Hilferty type
approximations for the null distribution of the Blum, Kiefer and
Rosenblatt test of bivariate independence.  Journal of Statistical
Planning and Inference 128: 31-41.

which, as their titles imply, revisit the often-cited view that
the two tests don't differ much and supply a computable means
of producing P-values for the said test. Despite this mathematical-
statistical analysis, it is my impression, following internet
searches and email enquiries, that no other publicly available
program in any language implements this test. Still, absence of
evidence is not evidence of absence.

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