# On Estimation of Lr-Norms in Gaussian White Noise Models

arXiv: https://arxiv.org/abs/1710.03863 · HTML: https://mlsanity.com/paper/1710.03863/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2017.

## Built on by (most cited first, 3 of 3)

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- [Locally differentially private estimation of nonlinear functionals of discrete distributions](https://mlsanity.com/paper/2107.03940/) (2021)
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## Abstract (arXiv)

We provide a complete picture of asymptotically minimax estimation of Lr-norms (for any r≥ 1) of the mean in Gaussian white noise model over Nikolskii-Besov spaces. In this regard, we complement the work of Lepski, Nemirovski and Spokoiny (1999), who considered the cases of r=1 (with poly-logarithmic gap between upper and lower bounds) and r even (with asymptotically sharp upper and lower bounds) over H"older spaces. We additionally consider the case of asymptotically adaptive minimax estimation and demonstrate a difference between even and non-even r in terms of an investigator's ability to produce asymptotically adaptive minimax estimators without paying a penalty.