10 papers
Testing by Betting while Borrowing and Bargaining
Hongjian Wang, Wouter M. Koolen, Aaditya Ramdas
Testing by betting has been a cornerstone of the game-theoretic statistics literature. One bets against the null hypothesis, and the accumulated wealth quantifies the evidenc…
E-values and sequential power-one tests for monotonicity and unimodality
Hongjian Wang, Aaditya Ramdas
We develop e-values and e-processes testing the null hypothesis that a distribution over nonnegative integers is monotone, and that a distribution over integers is unimodal given a…
M-estimation with e-statistics
Hongjian Wang, Aaditya Ramdas
We present a theory of point estimation with e-statistics (e-values and e-processes) by introducing the "ME-estimator": the parameter that minimizes the corresponding e-statistic,…
Almost sure null bankruptcy of testing-by-betting strategies
Hongjian Wang, Shubhada Agrawal, Aaditya Ramdas
The bounded mean betting procedure serves as a crucial interface between the domains of (1) sequential, anytime-valid statistical inference, and (2) online learning and portfolio s…
Positive Semidefinite Matrix Supermartingales
Hongjian Wang, Aaditya Ramdas
We explore the asymptotic convergence and nonasymptotic maximal inequalities of supermartingales and backward submartingales in the space of positive semidefinite matrices. These a…
Sharp Matrix Empirical Bernstein Inequalities
Hongjian Wang, Aaditya Ramdas
We present two sharp, closed-form empirical Bernstein inequalities for symmetric random matrices with bounded eigenvalues. By sharp, we mean that both inequalities adapt to the unk…