6 papers · 1 filter
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…
Intrinsic dimension concentration inequalities for self-adjoint operators
Diego Martinez-Taboada, Aaditya Ramdas
We derive novel concentration inequalities for the operator norm of the sum of self-adjoint operators that do not explicitly depend on the underlying dimension of the operator, but…
Mean Estimation in Banach Spaces Under Infinite Variance and Martingale Dependence
Justin Whitehouse, Ben Chugg, Diego Martinez-Taboada +1
We consider estimating the shared mean of a sequence of heavy-tailed random variables taking values in a Banach space. In particular, we revisit and extend a simple truncation-base…