Understand
Given a random sample from a random variable $T$ which is bounded from above, $T\le\tau$ a.s., we define processes that are positive supermartingales if $E(T)\ge\mu$.
- Such processes are called test martingales.
- Tests of the supermartingale hypothesis implicitly test the hypothesis $H_0:E(T)\ge\mu$.
- We construct test martingales that lead to tests with power 1.
Built on
Wald, A. (1945), Sequential Tests of Statistical Hypotheses, Ann. Math. Stat. 16
1945
Earlier work this paper cites.
Dellacherie, C. and Meyer, P. (Transl. J.P. Wilson) (1982), Probabilities and Potential B, Theory of Martingales , North Holland
1982
Earlier work this paper cites.
Similar
Williams, D. (1991), Probability with martingales , Campridge Univ. Press
1991
Cited alongside, same era.
Durrett, R. (2010), Probability: Theory and Examples , Fourth Ed., Cambridge Univ. Press
2010
Cited alongside, same era.
Then
Shafer, G., Shen, A., Vereshchagin, N. and Vovk, V. (2011), Test martingales, Bayes factors and p p -values. Statistical Science 26
2011
Later among the works it cites.
Grünwald, P. (2016), Toetsen als gokken: een redelijk alternatief voor de p-waarde. NAW 5/17(4), 236–244
2016
Later among the works it cites.
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