Sample Complexities of Estimating Gumbel--Max Watermark Proportions with and without Reduction to Pivotal Statistics
Watermarking promises statistical traceability of large language model (LLM) uses, but real documents rarely arrive as purely human-written or purely LLM-generated. This motivates a quantitative question beyond detection: what proportion of a document is generated from a pre-specified watermarked LLM? We study this watermark proportion estimation problem under the Gumbel--max watermarking mechanism, treating the next-token prediction distributions as unknown and arbitrary nuisance parameters subject to a non-degeneracy condition. We compare two observation regimes: in the full observation regime, the estimator observes the pseudorandom vector and the selected token at each position; in th...
| Authors | Shuwen Chai, Qiaosen Wang |
|---|---|
| Primary category | math.ST |
| Published | 30 June 2026 |
| Last updated at source | 2 July 2026 |
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