Year: 2024
Type: preprint
Abstract: We present an information-theoretic lower bound for the problem of parameter estimation with time-uniform coverage guarantees. Via a new a reduction to sequential testing, we obtain stronger lower bounds that capture the hardness of the time-uniform setting. In the case of location model estimation, logistic regression, and exponential family models, our $Ω(\sqrt{n^{-1}\log \log n})$ lower bound is sharp to within constant factors in typical settings.
Source: arXiv (Cornell University)
Authors: Duchi, John C., Haque, Saminul
Institution: Stanford University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Office of Naval Research
Awards: G4720003262, G8876996369
OpenAlex ID: W4391835382