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作者：Steiner, Gregor; Steel, Mark F. J.
作者单位：University of Warwick
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作者：Larsson, Martin; Ruf, Johannes
作者单位：Carnegie Mellon University; University of London; London School Economics & Political Science; University of London; London School Economics & Political Science
摘要：We derive confidence intervals (CIs) and confidence sequences (CSs) for the classical problem of estimating a bounded mean. Our approach generalizes and improves on the celebrated Chernoff method, yielding the best closed-form empirical-Bernstein CSs and CIs (converging exactly to the oracle Bernstein width) as well as non-closed-form betting CSs and CIs. Our method combines new composite nonnegative (super) martingales with Ville's maximal inequality, with strong connections to testing by bet...
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作者：Catalano, Marta; Fasano, Augusto; Rebaudo, Giovanni
作者单位：University of Warwick; University of Turin
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作者：Zhang, Yi; Shao, Xiaofeng
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
摘要：The bandwidth-free tests for a multi-dimensional parameter have attracted considerable attention in econometrics and statistics literature. These tests can be conveniently implemented due to their tuning-parameter free nature and possess more accurate size as compared to the traditional heteroskedasticity and autocorrelation consistent-based approaches. However, when sample size is small/medium, these bandwidth-free tests exhibit large size distortion when both the dimension of the parameter a...
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作者：Greenland, Sander
作者单位：University of California System; University of California Los Angeles; University of California System; University of California Los Angeles
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作者：Jiang, Rong; Yu, Keming
作者单位：Shanghai Polytechnic University; Brunel University
摘要：We derive confidence intervals (CIs) and confidence sequences (CSs) for the classical problem of estimating a bounded mean. Our approach generalizes and improves on the celebrated Chernoff method, yielding the best closed-form empirical-Bernstein CSs and CIs (converging exactly to the oracle Bernstein width) as well as non-closed-form betting CSs and CIs. Our method combines new composite nonnegative (super) martingales with Ville's maximal inequality, with strong connections to testing by bet...
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作者：Mueller, Manuel M.; Reeve, Henry W. J.; Cannings, Timothy, I; Samworth, Richard J.
作者单位：University of Cambridge; University of Bristol; University of Edinburgh; Heriot Watt University; University of Edinburgh
摘要：Given a sample of covariate-response pairs, we consider the subgroup selection problem of identifying a subset of the covariate domain where the regression function exceeds a predetermined threshold. We introduce a computationally feasible approach for subgroup selection in the context of multivariate isotonic regression based on martingale tests and multiple testing procedures for logically structured hypotheses. Our proposed procedure satisfies a non-asymptotic, uniform Type I error rate gua...
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作者：Gruenwald, Peter; de Heide, Rianne; Koolen, Wouter
作者单位：Leiden University - Excl LUMC; Leiden University; Vrije Universiteit Amsterdam; University of Twente
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作者：Wang, Ruodu
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作者：Nguyen, Hien
作者单位：University of Queensland; University of Queensland
摘要：We derive confidence intervals (CIs) and confidence sequences (CSs) for the classical problem of estimating a bounded mean. Our approach generalizes and improves on the celebrated Chernoff method, yielding the best closed-form empirical-Bernstein CSs and CIs (converging exactly to the oracle Bernstein width) as well as non-closed-form betting CSs and CIs. Our method combines new composite nonnegative (super) martingales with Ville's maximal inequality, with strong connections to testing by bet...
