Bootstrap Estimation of Eigenvalues in Principal Components Analysis (Janice Gifford).
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.