Multivariate mean estimation with direction-dependent accuracy

Randomized Distributed Mean Estimation: Accuracy vs Communication

We consider the problem of estimating the arithmetic average of a finite collection of real vectors stored in a distributed fashion across several compute nodes subject to a communication budget constraint. Our analysis does not rely on any statistical assumptions about the source of the vectors. This problem arises as a subproblem in many applications, including reduceall operations within alg...

Estimation of the Multivariate Normal Mean under the Extended Reflected Normal Loss Function

Nonparametric adaptive time-dependent multivariate function estimation

We consider the nonparametric estimation problem of time-dependent multivariate functions observed in a presence of additive cylindrical Gaussian white noise of a small intensity. We derive minimax lower bounds for the L-risk in the proposed spatio-temporal model as the intensity goes to zero, when the underlying unknown response function is assumed to belong to a ball of appropriately construc...

Estimation Accuracy of Maximum Likelihood Direction Finding Using Large Arrays

This paper analyzes the performance of methods for estimating the parameters of narrowband signals arriving at an array of sensors. The so-called deterministic and stochastic maximum likelihood (ML) methods are considered. A performance analysis is carried out for nite number of snapshots but assuming that the array is composed of a suuciently large number, m, of sensors. Strong consistency of ...

Improved minimax estimation of a multivariate normal mean under heteroscedasticity

Consider the problem of estimating a multivariate normal mean with a known variance matrix, which is not necessarily proportional to the identity matrix. The coordinates are shrunk directly in proportion to their variances in Efron and Morris’ (J. Amer. Statist. Assoc. 68 (1973) 117–130) empirical Bayes approach, whereas inversely in proportion to their variances in Berger’s (Ann. Statist. 4 (1...