Merging sequential e-values via martingales
@inproceedings{Vovk2020MergingSE, title={Merging sequential e-values via martingales}, author={Vladimir Vovk and Ruodu Wang}, year={2020} }
We study the problem of merging sequential or independent e-values into one e-value for statistical decision making. We describe a class of e-value merging functions via martingales, and show that all merging methods for sequential e-values are dominated by such a class. In case of merging independent e-values, the situation becomes much more sophis-ticated, and we provide a general class of such merging functions based on reordered test martingales.
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References
SHOWING 1-10 OF 24 REFERENCES
E-values: Calibration, combination and applications
- Computer ScienceThe Annals of Statistics
- 2021
It is demonstrated that e-values are often mathematically more tractable; in particular, in multiple testing of a single hypothesis, e- Values can be merged simply by averaging them, which allows to develop efficient procedures using e- values for testing multiple hypotheses.
Test Martingales, Bayes Factors and p-Values
- Mathematics
- 2011
A nonnegative martingale with initial value equal to one measures evidence against a probabilistic hypothesis. The inverse of its value at some stopping time can be interpreted as a Bayes factor. If…
E-values as unnormalized weights in multiple testing
- Computer Science
- 2022
This work shows that standard weighted multiple testing methods are not required when the weights are not constants, but are themselves e-values obtained from independent data, which could result in a massive increase in power.
Combining P-Values Via Averaging
- MathematicsBiometrika
- 2020
This paper proposes general methods for the problem of multiple testing of a single hypothesis, with a standard goal of combining a number of $p$-values without making any assumptions about their…
Extreme negative dependence and risk aggregation
- Mathematics, Computer ScienceJ. Multivar. Anal.
- 2015
Safe Testing
- Economics2020 Information Theory and Applications Workshop (ITA)
- 2020
Sharing Fisherian, Neymanian and Jeffreys-Bayesian interpretations, S-values and safe tests may provide a methodology acceptable to adherents of all three schools.
Admissible anytime-valid sequential inference must rely on nonnegative martingales.
- Mathematics, Computer Science
- 2020
This work shows that martingales are also universal---all constructions of (composite) anytime $p-values, confidence sequences, or e-values must necessarily utilize nonnegative martingale, and provides several sophisticated examples, with special focus on the nonparametric problem of testing if a distribution is symmetric, where the new constructions render past methods inadmissible.
Testing by betting: A strategy for statistical and scientific communication
- Computer ScienceJournal of the Royal Statistical Society: Series A (Statistics in Society)
- 2021
A simpler way of reporting statistical evidence is introduced: report the outcome of a bet against the null hypothesis, which leads to a new role for likelihood, to alternatives to power and confidence, and to a framework for meta‐analysis that accommodates both planned and opportunistic testing of statistical hypotheses and probabilistic forecasts.
On Tables of Random Numbers
- Mathematics
- 1993
The editors of Semiotika i Informatika have felt it appropriate to publish a Russian translation of my article, which reflects a certain stage of my attempts to give meaning to the frequency…
E-values: Calibration, combination, and applications
- Computer Science
- 2019
It is demonstrated that e-values are often mathematically more tractable; in particular, in multiple testing of a single hypothesis, e- Values can be merged simply by averaging them, which allows to develop efficient procedures using e- values for testing multiple hypotheses.