Bootstrap Estimation of Eigenvalues in Principal Components Analysis (Janice Gifford).
The students in Gifford's 1990 group were Vivek Goyal (University of Iowa, '92), Marcel Grenier (E.Conn. St. U., '92), Laura Kay Gross (Yale, '92), Jane Henley (MHC, '91). The group began by improving and expanding the programs written by the 1988 group. They simulated data from normal, uniform, and a variety of skewed distributions. They also focused their attention on the case where the last two eigenvalues are fairly close in size, but are not identically equal. They found that the bias-corrected confidence interval proposed by Efron performed clearly better than the standard confidence interval when the data are non-normal and when the true eigenvalues are clearly different in size. (Standard confidence intervals are generally too wide for uniform data, too narrow for skewed.) However, when the true eigenvalues are close in size, coverage for the bootstrap confidence intervals is systematically too low. Gross presented a paper at the AMS-MAA 1991 special session on research by undergraduates.