Basu: when an ancillary statistic is independent of a sufficient summary

What changed

Scientific scope

Connects bounded completeness and sufficiency to independence of every parameter-distribution-invariant statistic within the stated model, with a short general argument and distribution-theory illustrations. The exact target is Theorem 2 under the measurable-family and conditional-probability/sufficiency definitions of original 377–379, together with its stated illustrative use. Bounded completeness is required; arbitrary sufficient statistics do not yield the converse, as the original explicitly warns. Independence holds for each member of the model family, with the source's almost-everywhere conventions; no simultaneous pointwise strengthening across every conditional event/parameter is asserted. Parameter-independent distribution is the meaning of ancillary here, not absence of all scientific information. The normal and Gamma examples retain their distribution/model assumptions. The paper's Gaussian characterization draws on Darmois's earlier result and its Gamma characterization invokes Laha; neither is newly attributed wholesale to this criterion. No independent proof reconstruction or formal verification is recorded. Later generalizations and every statistical use of completeness remain separate.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

Debabrata Basu · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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