(a) Coverage, and (b) average widths, of EigenPrism SNR 95% confidence intervals.
Experiments used n = 105, p =
5×105, θ2 +
σ2 = 104, Bernoulli(0.01)
design, and β with 10% non-zero, Gaussian
entries. Each boxplot summarizes the (a) coverage and (b) width for 20 different
β's, each of which is estimated
with 500 simulations. The whiskers of the boxplots extend to the maximum and
minimum points. The black dotted line in (a) is the 95% confidence lower-bound
for the lowest whisker in each plot assuming all CIs achieve exact coverage, and
the grey line shows nominal coverage.