Testing Hypotheses Generated by Constraints

Published Online:https://doi.org/10.1287/moor.2025.1129

References

  • [1] Agrawal S, Juneja S, Glynn P (2020) Optimal δ-correct best-arm selection for heavy-tailed distributions. Kontorovich A, Neu G, eds. Proc. 31st Internat. Conf. Algorithmic Learn. Theory, Proceedings of Machine Learning Research, vol. 117 (PMLR, New York), 61–110.Google Scholar
  • [2] Agrawal S, Juneja SK, Koolen WM (2021) Regret minimization in heavy-tailed bandits. Belkin M, Kpotufe S, eds. Proc. 34th Conf. Learn. Theory, Proceedings of Machine Learning Research, vol. 134 (PMLR, New York), 26–62.Google Scholar
  • [3] Agrawal S, Koolen WM, Juneja S (2021) Optimal best-arm identification methods for tail-risk measures. Ranzato M, Beygelzimer A, Dauphin Y, Liang PS, Wortman Vaughan J, eds. Adv. Neural Inform. Processing Systems 34 NeurIPS 2021 (Curran Associates, Red Hook, NY), 25578–25590.Google Scholar
  • [4] Aliprantis CD, Border KC (2006) Infinite Dimensional Analysis, 3rd ed. (Springer, Berlin).Google Scholar
  • [5] Billingsley P (1999) Convergence of Probability Measures, 2nd ed. (John Wiley & Sons, Inc., New York).CrossrefGoogle Scholar
  • [6] Chernoff H (1952) A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Ann. Math. Statist. 23(4):493–507.CrossrefGoogle Scholar
  • [7] Clerico E (2024) Optimal e-value testing for properly constrained hypotheses. Preprint, submitted December 30, https://arxiv.org/abs/2412.21125.Google Scholar
  • [8] Clerico E (2025) On the optimality of coin-betting for mean estimation. Internat. J. Approximate Reasoning 187:109550.CrossrefGoogle Scholar
  • [9] Conway JB (1990) A Course in Functional Analysis, Graduate Texts in Mathematics, 2nd ed., vol. 96 (Springer-Verlag, New York).Google Scholar
  • [10] Cramér H (1994) Sur un nouveau théoreme-limite de la théorie des probabilités. Martin-Löf A, ed. Collected Works II (Springer, Berlin), 895–913.CrossrefGoogle Scholar
  • [11] Fan Y, Jiao Z, Wang R (2025) Testing the mean and variance by e-processes. Biometrika 112(1):asae049.CrossrefGoogle Scholar
  • [12] Grünwald P, de Heide R, Koolen WM (2024) Safe testing. J. Roy. Statist. Soc. Ser. B Methodology 86(4):1091–1128.CrossrefGoogle Scholar
  • [13] Howard SR, Ramdas A, McAuliffe J, Sekhon J (2020) Time-uniform Chernoff bounds via nonnegative supermartingales. Probab. Surveys 17:257–317.CrossrefGoogle Scholar
  • [14] Howard SR, Ramdas A, McAuliffe J, Sekhon J (2021) Time-uniform, nonparametric, nonasymptotic confidence sequences. Ann. Statist. 49(2):1055–1080.CrossrefGoogle Scholar
  • [15] Kelley JL (1975) General Topology, Graduate Texts in Mathematics, vol. 27 (Springer-Verlag, New York).Google Scholar
  • [16] Koning NW (2023) Post-hoc and anytime valid permutation and group invariance testing. Preprint, submitted October 2, https://arxiv.org/abs/2310.01153.Google Scholar
  • [17] Koning NW (2024) Continuous testing: Unifying tests and e-values. Preprint, submitted September 9, https://arxiv.org/abs/2409.05654.Google Scholar
  • [18] Krantz SG, Parks HR (2002) A Primer of Real Analytic Functions, 2nd ed. (Birkhäuser Boston, Inc., Boston).CrossrefGoogle Scholar
  • [19] Larsson M, Ramdas A, Ruf J (2025) The numeraire e-variable and reverse information projection. Ann. Statist. 53(3):1015–1043.CrossrefGoogle Scholar
  • [20] Maccheroni F, Marinacci M, Rustichini A (2006) Ambiguity aversion, robustness, and the variational representation of preferences. Econometrica 74(6):1447–1498.CrossrefGoogle Scholar
  • [21] Orabona F, Jun KS (2023) Tight concentrations and confidence sequences from the regret of universal portfolio. IEEE Trans. Inform. Theory 70(1):436–455.CrossrefGoogle Scholar
  • [22] Pandeva T, Forré P, Ramdas A, Shekhar S (2024) Deep anytime-valid hypothesis testing. Dasgupta S, Mandt S, Li Y, eds. Proc. 27th Internat. Conf. Artificial Intelligence Statist., Proceedings of Machine Learning Research, vol. 238 (PMLR, New York), 622–630.Google Scholar
  • [23] Pérez-Ortiz MF, Lardy T, de Heide R, Grünwald PD (2024) E-statistics, group invariance and anytime-valid testing. Ann. Statist. 52(4):1410–1432.CrossrefGoogle Scholar
  • [24] Podkopaev A, Ramdas A (2023) Sequential predictive two-sample and independence testing. Oh A, Naumann T, Globerson A, Saenko K, Hardt M, Levine S, eds. Adv. Neural Inform. Processing Systems 36 NeurIPS 2023 (Curran Associates, Red Hook, NY), 53275–53307.Google Scholar
  • [25] Podkopaev A, Blöbaum P, Kasiviswanathan S, Ramdas A (2023) Sequential kernelized independence testing. Krause A, Brunskill E, Cho K, Engelhardt B, Sabato S, Scarlett J, eds. Proc. 40th Internat. Conf. Machine Learn., Proceedings of Machine Learning Research, vol. 202 (PMLR, New York), 27957–27993.Google Scholar
  • [26] Ramdas A, Wang R (2025) Hypothesis testing with e-values. Foundations Trends Statist. 1(1–2):1–390.CrossrefGoogle Scholar
  • [27] Ramdas A, Ruf J, Larsson M, Koolen W (2020) Admissible anytime-valid sequential inference must rely on nonnegative martingales. Preprint, submitted September 7, https://arxiv.org/abs/2009.03167.Google Scholar
  • [28] Ramdas A, Ruf J, Larsson M, Koolen WM (2022) Testing exchangeability: Fork-convexity, supermartingales and e-processes. Internat. J. Approximate Reasoning 141:83–109.CrossrefGoogle Scholar
  • [29] Rockafellar R, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J. Banking Finance 26(7):1443–1471.CrossrefGoogle Scholar
  • [30] Romano JP, Shaikh AM, Wolf M (2014) A practical two-step method for testing moment inequalities. Econometrica 82(5):1979–2002.CrossrefGoogle Scholar
  • [31] Saha A, Ramdas A (2024) Testing exchangeability by pairwise betting. Dasgupta S, Mandt S, Li Y, eds. Proc. 27th Internat. Conf. Artificial Intelligence Statist., Proceedings of Machine Learning Research, vol. 238 (PMLR, New York), 4915–4923.Google Scholar
  • [32] Schaefer HH, Wolff MP (1999) Topological Vector Spaces, Graduate Texts in Mathematics, 2nd ed., vol. 3 (Springer-Verlag, New York).CrossrefGoogle Scholar
  • [33] Shafer G (2021) Testing by betting: A strategy for statistical and scientific communication. J. Roy. Statist. Soc. Ser. A Statist. Soc. 184(2):407–431.CrossrefGoogle Scholar
  • [34] Shekhar S, Ramdas A (2023) Nonparametric two-sample testing by betting. IEEE Trans. Inform. Theory 70(2):1178–1203.CrossrefGoogle Scholar
  • [35] Vovk V (2021) Testing randomness online. Statist. Sci. 36(4):595–611.CrossrefGoogle Scholar
  • [36] Vovk V, Wang R (2021) E-values: Calibration, combination and applications. Ann. Statist. 49(3):1736–1754.CrossrefGoogle Scholar
  • [37] Wang H, Ramdas A (2023) Catoni-style confidence sequences for heavy-tailed mean estimation. Stochastic Processes Appl. 163:168–202.CrossrefGoogle Scholar
  • [38] Wang Q, Wang R, Ziegel J (2025) E-backtesting. Management Sci., ePub ahead of print September 23, https://doi.org/10.1287/mnsc.2023.01659.Google Scholar
  • [39] Wasserman L, Ramdas A, Balakrishnan S (2020) Universal inference. Proc. Natl. Acad. Sci. USA 117(29):16880–16890.CrossrefGoogle Scholar
  • [40] Waudby-Smith I, Ramdas A (2024) Estimating means of bounded random variables by betting. J. Roy. Statist. Soc. Ser. B Statist. Methodology 86(1):1–27.CrossrefGoogle Scholar
  • [41] Willard S (1970) General Topology (Addison-Wesley Publishing Co., Reading, MA).Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.