Corpus ID: 227239090

Minimax bounds for estimating multivariate Gaussian location mixtures.

@article{Kim2020MinimaxBF,
  title={Minimax bounds for estimating multivariate Gaussian location mixtures.},
  author={Arlene K. H. Kim and Adityanand Guntuboyina},
  journal={arXiv: Statistics Theory},
  year={2020}
}
We prove minimax bounds for estimating Gaussian location mixtures on $\mathbb{R}^d$ under the squared $L^2$ and the squared Hellinger loss functions. Under the squared $L^2$ loss, we prove that the minimax rate is upper and lower bounded by a constant multiple of $n^{-1}(\log n)^{d/2}$. Under the squared Hellinger loss, we consider two subclasses based on the behavior of the tails of the mixing measure. When the mixing measure has a sub-Gaussian tail, the minimax rate under the squared… Expand
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