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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, February 18, 2003}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Iain Johnstone}
\centerline{\sl Stanford University}
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\centerline{\bf Approximations for the largest canonical correlation}
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Given n observations on two groups of variables, say X and Y,
the classical technique of canonical correlations seeks linear
combinations of the X and Y variable sets that are most highly
correlated.  The associated (generalized) eigenvalue problem is basic
to a variety of multivariate methods, both ancient and modern.

The null distribution of the largest canonical correlation, though
well known, is difficult to work with in practice.  An asymptotic
regime in which the number of X and Y variables are comparable to
n leads to a simple approximation using the Tracy-Widom
distribution. Being second-order accurate under the classical
assumptions, the approximation turns out to be informative, and
perhaps preferable to those in current software, even on textbook size
examples.

This work is joint with Peter Forrester of the University of Melbourne.

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