Validity of the ordinary bootstrap at exact tangency

Establish whether ordinary-bootstrap confidence intervals provide valid inference for the curvature-overstatement parameter at the exact tangency boundary.

Background

The paper develops regular delta-method inference for the curvature-overstatement parameter when the quadratic threshold is separated from tangency. At tangency, however, the estimator has nonstandard behavior: it may be undefined with positive probability, converges at an n^{1/4} rate, and has a non-Gaussian limit. These features create a boundary problem for resampling-based inference.

A percentile bootstrap shows improved finite-sample coverage in simulations near tangency, but the paper does not establish its validity at the boundary itself. The authors therefore leave unresolved whether the ordinary bootstrap can consistently approximate the distribution or deliver correctly calibrated confidence intervals under exact tangency.