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…
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…
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…
Nonasymptotic Heavy-Tailed Mean Estimation in Smooth Banach Spaces
Justin Whitehouse, Ben Chugg, Diego Martinez-Taboada +1
We consider the problem of nonasymptotic mean estimation for heavy-tailed random variables taking values in a smooth Banach space. In particular, we extend and improve a simple tru…
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…