# Estimation of smooth functionals of covariance operators: jackknife bias reduction and bounds in terms of effective rank

@inproceedings{Koltchinskii2022EstimationOS, title={Estimation of smooth functionals of covariance operators: jackknife bias reduction and bounds in terms of effective rank}, author={Vladimir Koltchinskii}, year={2022} }

: Let E be a separable Banach space and let X,X 1 ,...,X n ,... be i.i.d. Gaussian random variables taking values in E with mean zero and unknown covariance operator Σ : E ∗ 7→ E. The complexity of estimation of Σ based on observations X 1 ,...,X n is naturally characterized by the so called eﬀective rank of Σ : r (Σ) := E Σ k X k 2 k Σ k , where k Σ k is the operator norm of Σ . Given a smooth real valued functional f deﬁned on the space L ( E ∗ ,E ) of symmetric linear operators from E ∗ into…

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