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Re: st: Partial Correlation Kendall's Tau (or Somers D)


From   Stas Kolenikov <[email protected]>
To   [email protected]
Subject   Re: st: Partial Correlation Kendall's Tau (or Somers D)
Date   Wed, 21 Jan 2009 08:28:46 -0600

Al,

there are three types of statisticians: those who can count to four
and those who cannot :)).

Since the original tau's are U-statistics, they will have a (joint
multivariate) asymptotic normal distribution, and hence the
partialized version you presented would also be asymptotically normal.
The necessary condition for the jackknife standard errors to be
consistent is that the statistic of interest has an asymptotically
normal distribution, and I would guess that other more subtle
regularity conditions would also be satisifed (although jackknife is
not consistent say for a median which is also asymptotically normal).
If you have a complex survey design then you would need to omit the
complete PSU when computing the standard errors, and Stata's -svy
jackknife- does that for you (although you would  need to write a
wrapper of -eclass, properties(svyj)- and see that the conditions
outlined for those properties are satisfied).

You guys do have some powerful computers at NASA, I guess. I wouldn't
think of doing jackknife over -ktau- with the capacities I have :)).

On 1/21/09, Feiveson, Alan H. (JSC-SK311) <[email protected]> wrote:
> Hi - I have been reading in Gibbons and Chakraborti (Nonparametric
>  Statistical Inference) about a Kendall's Tau analog to partial
>  correlation, where one would like to quantify the association between y
>  and x after correcting for z. Specifically, the authors define tau_xy.z
>  in terms of the three pairwise associations tau_xy, tau_yz, and tau_xz,
>  and then give an expression that loooks exaclty like Pearson partial
>  correlation:
>
>
>  tau_xy.z = (tau_xy - tau_xz*tau_yz)/sqrt((1-tau_xz^2)*(1-tau_yz^2))
>
>
>  My questions on this are
>
>  1. Can the jackknife method for standard errors be extended to tau_xy.z
>  or its Somers D analog?
>
>  3. Are there extensions to defining tau_xy.z within or betwen strata and
>  for obtaining standard errors with clusters as Roger Newson has done?
>
>  4. Most importantly - Roger - do you have any plans for updating your
>  Somers D program to include partial association?
>
>  Thanks,
>
>  Al Feiveson
>

-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.
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