9 papers
Gaussian-efficient testing by betting on the mean of bounded data
Diego Martinez-Taboada, Aaditya Ramdas
Given -valued random variables such that for all , we propose a new nonasymptotic confidence interval for tha…
Bentkus-type asymptotic e-values
Diego Martinez-Taboada, Ben Chugg, Aaditya Ramdas
Asymptotic e-values are emerging as a powerful alternative to asymptotic p-values, particularly in post-hoc inference and multiple testing, where significance levels may be data-de…
Sharp Empirical Bernstein Bounds for the Variance of Bounded Random Variables
Diego Martinez-Taboada, Aaditya Ramdas
We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further…
Empirical Bernstein in smooth Banach spaces
Diego Martinez-Taboada, Aaditya Ramdas
Existing concentration bounds for bounded vector-valued random variables include extensions of the scalar Hoeffding and Bernstein inequalities. While the latter is typically tighte…
Intrinsic-dimension empirical Bernstein inequalities for bounded self-adjoint operators
Diego Martinez-Taboada, Aaditya Ramdas
Operator-valued concentration inequalities are foundational to the analysis of modern high-dimensional statistics and randomized algorithms. However, standard oracle bounds are fre…
Vector-valued self-normalized concentration inequalities beyond sub-Gaussianity
Diego Martinez-Taboada, Tomas Gonzalez, Aaditya Ramdas
The study of self-normalized processes plays a crucial role in a wide range of applications, from sequential decision-making to econometrics. While the behavior of self-normalized…