5 papers · 1 filter
Risk reversal for least squares estimators under nested convex constraints
Omar Al-Ghattas
In constrained stochastic optimization, one expects that restricting the feasible set, provided it still contains the true parameter, should not increase the statistical risk of th…
On the Estimation of Gaussian Moment Tensors
Omar Al-Ghattas, Jiaheng Chen, Daniel Sanz-Alonso
This paper studies two estimators for Gaussian moment tensors: the standard sample moment estimator and a plug-in estimator based on Isserlis's theorem. We establish dimension-free…
Optimal Estimation of Structured Covariance Operators
Omar Al-Ghattas, Jiaheng Chen, Daniel Sanz-Alonso +1
This paper establishes optimal convergence rates for estimation of structured covariance operators of Gaussian processes. We study banded operators with kernels that decay rapidly…
Covariance Operator Estimation via Adaptive Thresholding
Omar Al-Ghattas, Daniel Sanz-Alonso
This paper studies sparse covariance operator estimation for nonstationary processes with sharply varying marginal variance and small correlation lengthscale. We introduce a covari…
Covariance Operator Estimation: Sparsity, Lengthscale, and Ensemble Kalman Filters
Omar Al-Ghattas, Jiaheng Chen, Daniel Sanz-Alonso +1
This paper investigates covariance operator estimation via thresholding. For Gaussian random fields with approximately sparse covariance operators, we establish non-asymptotic boun…