8 papers
Beyond Wald's Equation and the Optional Sampling Theorem
Michael J. Klass, Victor H. de la Pena
This paper establishes a conservation identity for mean-zero martingales stopped by extended-valued stopping times. For any mean-zero martingale and any extended-valued s…
Mitigating the Winner's Curse While Controlling Multiplicity: e-Process Methods for Anytime-Valid Inference in Dose-Ranging Trials
Victor K. de la Pena, Fangyuan Lin, Demissie Alemayehu +1
Phase II dose-ranging trials often report the largest observed dose-control effect while inspecting accumulating data repeatedly. This creates two coupled distortions: selection op…
The Exact Ville Identity: From the Absorbing Case to the General Law with an Application to E-Values
Victor H. de la Pena, Michael J. Klass
For a nonnegative supermartingale with , let be the first time it reaches a level . Ville's inequality gives only the bound …
Bounded Difference Concentration for Infinitely Exchangeable Sequences with Applications to AI Benchmark Uncertainty
Fangyuan Lin, Spencer Frei, Victor H. de la Pena
We consider the concentration properties of functions of infinitely exchangeable random variables. By conditioning on the de Finetti directing measure, we show that the deviation o…
A Selection Premium Decomposition for the Expected Maximum of Random Walks
Victor H. de la Pena, Fangyuan Lin, Victor K. de la Pena
When models are evaluated on the same validation set of size , the selected winner's apparent performance is biased upward. Suppose models are evaluated on a shared sequ…
Decoupling for Markov Chains
Nawaf Bou-Rabee, Victor H. de la Peña
Consider a Markov chain with invariant measure that admits the representation , where are i.i.d. random variables and …