Fetching the paper…
Reading the bibliography…
Given a composite null $ \mathcal P$ and composite alternative $ \mathcal Q$, when and how can we construct a p-value whose distribution is exactly uniform under the null, and stochastically smaller than uniform under the alternative? Similarly, when and how can we construct an e-value whose expectation exactly equals one under the null, but its expected logarithm under the alternative is positive? We answer these basic questions, and other related ones, when $ \mathcal P$ and $ \mathcal Q$ are convex polytopes (in the space of probability measures).
[author] Wiener, NorbertN. (1933). The Fourier Integral and Certain of its Applications. Cambridge University Press
1933
Earlier work this paper cites.
1938
Earlier work this paper cites.
[author] Berger, AgnesA. (1951). On uniformly consistent tests. The Annals of Mathematical Statistics 22 289–293
1951
Earlier work this paper cites.
[author] Kraft, CharlesC. (1955). Some conditions for consistency and uniform consistency of statistical procedures. University of California Publication in Statistics 2 125–141
1955
Earlier work this paper cites.
[author] Kelly, J. L.J. L. (1956). A new interpretation of information rate. Bell System Technical Journal 917–926
1956
Earlier work this paper cites.
[author] Hoeffding, WassilyW. and Wolfowitz, JJ. (1958). Distinguishability of sets of distributions. The Annals of Mathematical Statistics 29 700–718
1958
Earlier work this paper cites.
[author] Breiman, LeoL. (1961). Optimal gambling systems for favorable games. Proc. Fourth Berkeley Symposium on Probability and Mathematical Statistics
1961
Earlier work this paper cites.
[author] Strassen, VolkerV. (1965). The existence of probability measures with given marginals. The Annals of Mathematical Statistics 36 423–439
1965
Earlier work this paper cites.
[author] Darling, Donald A.D. A. and Robbins, HerbertH. (1967). Confidence sequences for mean, variance, and median. Proceedings of the National Academy of Sciences of the United States of America 58 66–68
1967
Earlier work this paper cites.
[author] Rockafellar, R TyrrellR. T. (1970). Convex Analysis 18. Princeton University Press
1970
Earlier work this paper cites.
[author] Simons, GordonG. (1970). A martingale decomposition theorem. The Annals of Mathematical Statistics 41 1102–1104
1970
Earlier work this paper cites.
[author] Robbins, HerbertH. and Siegmund, DavidD. (1974). The expected sample size of some tests of power one. The Annals of Statistics 2 415–436
1974
Earlier work this paper cites.
[author] Bell, RobertR. and Cover, Thomas MT. M. (1988). Game-theoretic optimal portfolios. Management Science 34 724–733
1988
Earlier work this paper cites.
[author] Conway, John BJ. B. (1990). A Course in Functional Analysis 96. Springer
1990
Earlier work this paper cites.
[author] Talagrand, MichelM. (1996). New concentration inequalities in product spaces. Inventiones Mathematicae 126 505–563
1996
Earlier work this paper cites.
[author] Sato, Ken-ItiK.-I. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press
1999
Cited alongside, same era.
[author] Shafer, GlennG. and Vovk, VladimirV. (2001). Probability and Finance: It’s Only a Game. Wiley, New York
2001
Cited alongside, same era.
[author] Shaked, MosheM. and Shanthikumar, J GeorgeJ. G. (2007). Stochastic Orders. Springer
2007
Cited alongside, same era.
2009
Cited alongside, same era.
[author] Villani, CédricC. (2009). Optimal Transport: Old and New 338. Springer
2009
Cited alongside, same era.
[author] Shafer, GlennG. (2021). Testing by betting: a strategy for statistical and scientific communication (with discussion and response). Journal of the Royal Statistic Society A 184 407–478
2021
Later among the works it cites.
[author] Vovk, VladimirV. (2021). Testing randomness online. Statistical Science 36 595–611
2021
Later among the works it cites.
[author] Vovk, VladimirV. and Wang, RuoduR. (2021). E-values: Calibration, combination, and applications. Annals of Statistics 49 1736–1754
2021
Later among the works it cites.
2022
Later among the works it cites.
[author] Ramdas, AadityaA., Ruf, JohannesJ., Larsson, MartinM. and Koolen, Wouter MW. M. (2022). Testing exchangeability: fork-convexity, supermartingales and e-processes. International Journal of Approximate Reasoning 141 83–109
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
[author] Shafer, GlennG., Shen, AlexanderA., Vereshchagin, NikolaiN. and Vovk, VladimirV. (2011). Test martingales, Bayes factors and p-values. Statistical Science 26 84–101
2011
Cited alongside, same era.
[author] Simon, BarryB. (2011). Convexity: an Analytic Viewpoint 187. Cambridge University Press
2011
Cited alongside, same era.
[author] Teschl, GeraldG. (2012). Ordinary Differential Equations and Dynamical Systems 140. American Mathematical Soc
2012
Cited alongside, same era.
[author] Kühnel, WolfgangW. (2015). Differential Geometry 77. American Mathematical Soc
2015
Cited alongside, same era.
[author] Santambrogio, FilippoF. (2015). Optimal Transport for Applied Mathematicians 55. Birkäuser, NY
2015
Cited alongside, same era.
[author] Shafer, GlennG. and Vovk, VladimirV. (2019). Game-Theoretic Foundations for Probability and Finance. Wiley, Hoboken, New Jersey
2019
Cited alongside, same era.
[author] Shen, JieJ., Shen, YiY., Wang, BinB. and Wang, RuoduR. (2019). Distributional compatibility for change of measures. Finance and Stochastics 23 761–794
2019
Cited alongside, same era.
2022
Later among the works it cites.
[author] Wang, RuoduR. and Ramdas, AadityaA. (2022). False discovery rate control with e-values. Journal of the Royal Statistical Society: Series B (Statistical Methodology)
2022
Later among the works it cites.
2023
Closest in time.
2023
Closest in time.
[author] Ramdas, AadityaA., Grünwald, PeterP., Vovk, VladimirV. and Shafer, GlennG. (2023). Game-theoretic statistics and safe anytime-valid inference. Statistical Science
2023
Closest in time.
2023
Closest in time.
[author] Grünwald, P.P., de Heide, RianneR. and Koolen, WouterW. (2024). Safe testing. Journal of the Royal Statistical Society, Series B
2024
Closest in time.
2024
Closest in time.
[author] Vovk, VladimirV. and Wang, RuoduR. (2024). Nonparametric e-tests of symmetry. New England Journal on Statistics and Data Science 1–10
2024
Closest in time.
[author] Waudby-Smith, IanI. and Ramdas, AadityaA. (2024). Estimating means of bounded random variables by betting. Journal of the Royal Statistical Society Series B: Statistical Methodology 86 1–27
2024
Closest in time.