A tapered sample cumulant estimator is minimax rate-optimal for bandable higher-order cumulant tensors under spectral norm when the bandwidth is near the oracle value and the sample size is sufficiently large.
Asymptotic theory for estimators of high-order statistics of stationary processes.IEEE Transactions on Information Theory, 64(7):4907–4922, 2018
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Bandable Cumulant Tensors: Optimal Estimation and Applications in Non-Gaussian Data Modeling
A tapered sample cumulant estimator is minimax rate-optimal for bandable higher-order cumulant tensors under spectral norm when the bandwidth is near the oracle value and the sample size is sufficiently large.