4 papers · 1 filter
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…
The extended Ville's inequality for nonintegrable nonnegative supermartingales
Hongjian Wang, Aaditya Ramdas
Following the initial work by Robbins, we rigorously present an extended theory of nonnegative supermartingales, requiring neither integrability nor finiteness. In particular, we d…