Extend the certificate to general sub-Gaussian noise

Extend the data-driven aggregation-bias certificate, which currently relies on exact Gaussian noise deconvolution, to settings with general sub-Gaussian observation noise.

Background

The aggregation-bias certificate estimates the maximum-minus-mean gap within a tree cell from noisy random-path probes. Its deconvolution step uses the exact Gaussian moment-generating function to recover an upper bound on the moment-generating function of the latent leaf means. The paper notes that a sub-Gaussian upper bound on the noise moment-generating function gives a lower bound in the wrong direction, so the existing proof does not extend directly to general sub-Gaussian noise.