Hoeffding: bounded-sum concentration and convex sampling comparison

What changed

Scientific scope

Hoeffding organized finite tail bounds for bounded independent sums, extended a range-only bound to unequal intervals, and transferred exponential bounds to explicitly represented dependent statistics and finite-population sampling. The concentration bounds apply to the specified independent bounded variables and separately treated sampling settings. Bounded ranges, means and dependence assumptions cannot be omitted. The bounds are distribution-free within those conditions, not a proof for arbitrary adaptive/dependent sequences. Later martingale formulations and the withheld Azuma record are not silently credited here.

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

Wassily Hoeffding · 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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