Optimal rates of convergence for convex set estimation from support functions

Optimal Rates of Convergence for Convex Set Estimation from Support Functions by Adityanand Guntuboyina

The function hK is called the support function of K because it provides information on support hyperplanes and halfspaces of K . Indeed, every support halfspace of K is of the form {x :x · u≤ hK(u)} for some u ∈ Sd−1 and since K equals the intersection of all its support halfspaces, the function hK uniquely determines K . For a proof of this and other elementary properties of the support functi...

Convergence Rates of the Ellipsoid Method on General Convex Functions

Optimal Rates of Convergence for Sparse Covariance Matrix Estimation By

This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman divergence losses. A major focus is on the derivation of a rate sharp minimax lower bound. The problem exhibits new features that are significantly different from those that occur in the conventional nonparametric function estimation pro...

Optimal Rates of Convergence for Sparse Covariance Matrix Estimation

This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman divergence losses. A major focus is on the derivation of a rate sharp minimax lower bound. The problem exhibits new features that are significantly different from those that occur in the conventional nonparametric function estimation pro...

Optimal Rates of Convergence for Covariance Matrix Estimation

Covariance matrix plays a central role in multivariate statistical analysis. Significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices. However, a minimax theory has yet been developed. In this paper we establish the optimal rates of convergence for estimating the covariance matrix under both the operator norm and Frobenius n...