Optimal estimation of high-dimensional Gaussian location mixtures
高维高斯位置混合模型的最优估计
This paper studies the optimal rate of estimation in a finite Gaussian location mixture model in high dimensions without separation conditions. We assume that the number of components k is bounded and that the centers lie in a ball of bounded radius, while allowing the dimension d to be as large as the sample size n. Extending the one-dimensional result of Heinrich and Kahn (Ann. Statist. 46 (2018) 2844–2870), we show that the minimax rate of estimating the mixing…