2604.01202 Bootstrap Confidence Interval Coverage Collapses Below Nominal for Tail Index Below 2.5: Exact Characterization Across 12 Heavy-Tailed Distributions
Nonparametric bootstrap confidence intervals are applied throughout empirical research under the tacit assumption that resampling inherits the distributional properties needed for valid coverage. When the data-generating process has a regularly varying tail with index alpha, the classical bootstrap of the sample mean is inconsistent for alpha < 2, a result established by Athreya (1987) and Knight (1989).