bibkey: “chanwalther2015aligned” authors: “Hock Peng Chan; Guenther Walther” year: 2015 title: “Optimal detection of multi-sample aligned sparse signals” doi: “10.1214/15-AOS1328” url: “https://arxiv.org/abs/1510.03659v1” claim: “Section 3.1 constructs an average likelihood ratio by evaluating component likelihoods at the asymptotic detectable boundary; Theorem 4 proves asymptotic separation with fixed sparsity-exponent slack in the independent Gaussian aligned-signal model.” strata_touched: [] license: “citation-only” triage: “anchor”

Optimal detection of multi-sample aligned sparse signals

Annals of Statistics 43(5), 1865–1895 (2015). The inspected source is arXiv:1510.03659v1, a 32-page PDF. Model (2.2), PDF page 3, uses independent standard Gaussian errors and independent Bernoulli indicators for which sequences contain an aligned signal interval. Equation (2.4) specifies the asymptotic ratio of sequence length to signal length.

Section 3.1, PDF page 9, explicitly substitutes the asymptotic detectable boundary for the unknown mean when forming the component likelihoods; it then integrates over a sparsity parameter and averages across intervals. Theorem 4 on that page assumes a mean at its displayed boundary and signal probability N^(-beta+epsilon), with fixed 0 < beta < 1 and 0 < epsilon <= beta. It obtains a statistic diverging in alternative probability, allowing the sum of Type I and Type II errors to tend to zero.

Evaluating likelihoods at a detection boundary is therefore literature-attested. The theorem does not provide an exact nondegenerate critical-risk curve, a fixed single-spike prior, a full Markov path, or uniform control at a bounded-amplitude endpoint. The parity-kernel adaptation must separately establish the true-law score mean and variance under the chosen surrogate amplitude, endpoint KL control, and the necessary and sufficient clipping conditions within its specified rule family. Those are model-specific repo-derived deductions, not a claim that boundary calibration itself is new.