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From charlie@umnstat.stat.umn.edu Wed Jan  6 08:18 PST 1993
From: "Charles Geyer" <charlie@umnstat.stat.umn.edu>
To: flim@weber.ucsd.edu
Subject: Re: ACE (Alternating Conditional Expectations)
Newsgroups: sci.math.stat
Organization: School of Statistics, University of Minnesota

In article <1ib1luINN84d@network.ucsd.edu> you write:
>Hello netters. I have a simple ACE (Breiman and Friedman 1985) question.
>
>ACE stands for Alternating Conditional Expectations, and is a method
>of estimating the relationship between the explanatory and response
>variables, transforming the variables to maximize their correlation.
>
>The presumed relationship between Y and X, for example, is
>
>	\theta(Y) = \phi(X) + e
>
>where e is random error.
>
>One can use either BLSS or S to invoke ACE.
>For both statistical packages, I found that \hat{\theta}(Y) did NOT
>equal \hat{\phi}(X), where \hat symbolizes the estimated
>transformations.
>
>In fact, \hat{\theta}(Y) was not even proportional to \hat{\phi}(X).



You said it yourself

   \theta(Y) - \phi(X)

is the residuals -- random error.

You might find the output simpler to understand if you use the option
to disallow nonlinear transformations of the response.  Then you get

   Y = phi(X) + error

and it looks much more like the usual regression situation.  You don't
then expect Y to be proportional to phi(X).  [Actually it won't do this
it insists on at least a standardizing linear transformation of Y, but
the points the same.]

-- 
Charles Geyer
School of Statistics
University of Minnesota
charlie@umnstat.stat.umn.edu

================================================

Thanks Charles, yes it all makes sense. ACE attempts to maximize
the correlation between \theta(Y) and \phi(X).
Thus if \hat{\theta}(Y) were proportional to \hat{\phi}(X),
the sample correlation would be 1. This would happen only in
extreme cases! Thanks again.
-- 
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      FRANCIS W. LIM  |  email: flim@ucsd.edu | dept phone: (619) 534-3383
      Dept of Economics, Univ of Cal at San Diego, La Jolla, CA 92093-0508
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