bibkey: “halljin2010innovated” authors: “Peter Hall; Jiashun Jin” year: 2010 title: “Innovated higher criticism for detecting sparse signals in correlated noise” doi: “10.1214/09-AOS764” url: “https://arxiv.org/abs/0902.3837v2” claim: “Theorem 2.1 gives adaptive full power above the sparse Gaussian detection boundary for an exactly specified but growing support size, with locations sampled uniformly without replacement.” strata_touched: [] license: “citation-only” triage: “anchor”

Innovated higher criticism for detecting sparse signals in correlated noise

The Annals of Statistics 38(3), 1686–1732 (2010), DOI 10.1214/09-AOS764. The inspected source is the 49-page arXiv:0902.3837v2 PDF, revised 4 October 2010. Its first page gives the journal pagination and DOI; Crossref corroborates the title, authors, year, journal, volume and issue.

Equation (2.2), PDF page 3, sets the exact number of nonzero coordinates to m = n^(1-beta), with fixed 1/2 < beta < 1. Thus the cardinality is deterministic at each dimension and grows to infinity. Equation (2.3), page 4, draws the support uniformly without replacement. The principal model gives all nonzero coordinates a common Gaussian mean magnitude. The discussion following (2.4) also allows independent random nonnegative strength multipliers; it retains the growing support count.

Theorem 2.1, PDF page 6, treats independent Gaussian noise. Higher Criticism has asymptotically full power for every fixed (beta,r) strictly inside r > rho_*(beta), using a rule that knows neither parameter. The surrounding argument also gives vanishing type I error. The paper then treats correlated noise; its later covariance-dependent boundaries must not be silently identified with the independent-noise curve.

Exact cardinality without replacement and adaptation to unknown sparsity and strength are therefore literature-attested. This result does not treat a constant positive integer count, deterministic heterogeneous coordinatewise critical parameters, or their finite product-risk limit. The compensated parity-kernel likelihood comparison and stationary-path covariances require the separate repo-derived argument. No worldwide originality claim follows from these scope differences.