Minimax estimation of functionals in sparse vector model with correlated observations
Abstract
We consider the observations of an unknown s-sparse vector θ corrupted by Gaussian noise with zero mean and unknown covariance matrix Σ. We propose minimax optimal methods of estimating the ℓ2 norm of θ and testing the hypothesis H0:θ=0 against sparse alternatives when only partial information about Σ is available, such as an upper bound on its Frobenius norm and the values of its diagonal entries to within an unknown scaling factor. We show that the minimax rates of the estimation and testing are leveraged not by the dimension of the problem but by the value of the Frobenius norm of Σ.
Fields of Study & Subjects
Statistical Methods and Inference
Publication details
- Journal / source
- Electronic Journal of Statistics
- Volume
- 20
- Issue
- 2
- Pages
- 3770–3806
- Publication date
- 1 January 2026
- Language
- EN