# 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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