Adityanand Guntuboyina

Lower Bounds for the Minimax Risk Using

Lower bounds involving f-divergences between the underlying probability measures are proved for the minimax risk in estimation problems. Our proofs just use simple convexity facts. Special cases and straightforward corollaries of our bounds include well known inequalities for establishing minimax lower bounds such as Fanos inequality, Pinskers inequality and inequalities based on global entropy conditions. Two applications are provided: a new minimax lower bound for the reconstruction of convex bodies from noisy support function measurements and a different proof of a recent minimax lower bound for the estimation of a covariance matrix.

f

We consider the problem of estimating an unknown

-Divergences, and Applications

\theta\in {\mathbb{R}}^n

On risk bounds in isotonic and other shape restricted regression problems

from noisy observations under the constraint that

Stochastically Transitive Models for Pairwise Comparisons: Statistical and Computational Issues

\theta

Sharp Inequalities for

belongs to certain convex polyhedral cones in

f

{\mathbb{R}}^n

-Divergences

. Under this setting, we prove bounds for the risk of the least squares estimator (LSE). The obtained risk bound behaves differently depending on the true sequence

OPTIMAL RATES OF CONVERGENCE FOR CONVEX SET ESTIMATION FROM SUPPORT FUNCTIONS

\theta

Adaptation in log-concave density estimation

which highlights the adaptive behavior of