REU 1988
The students in Gifford's group were Joe Gregorio
(E. Conn. St. Univ.), Susan Graveline (St. Michael's College), Greg
Labine (Western New England College) and Anne Sutherby (Holy Cross).
The group developed computer programs for simulating the sampling
distributions of eigenvalues under a variety of conditions. They
demonstrated that in the case of three normally distributed variables
the eigenvalues of the covariance matrix appear to have sampling
distributions that are roughly normal when sample sizes are at least
200. However, the sampling distributions are clearly not normal when
the variables are uniformly distributed. The group also wrote
programs for constructing bootstrap and standard confidence intervals
for the eigenvalues. They found that the simple percentile method for
constructing bootstrap confidence intervals was not adequate. They
researched and experimented with improvements on the construction of
confidence intervals. Gregorio gave a talk on the summer's project at
his home institution.
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