minimax optimal，同时\phi(\Theta)称为 minimax rate 注：这里 minimax rate只关心参数而不在乎常数，...
基本上现在流行的论文大多数都是渐近意义下的minimax，并且不在乎乘一个常数(所谓rate optimal)。精确的m...
The test constructed by non-parametric kernel techniques can be rate optimal when bandwidths are selected appropriately. Since bandwidths are often selected in a data-dependent way in empirical studies, the rate-optimality of the test with data-driven bandwidths is investigated. While least squares...
rate of convergence / error probability / modulus of continuity / multicategory classification Cite this article Download Citations Di Rong CHEN, Xu YOU. Minimax Optimal Rates of Convergence for Multicategory Classifications. Acta Mathematica Sinica, 2007, 23(8): 1419-1426 https://doi.org/10.10...
It is known that such a rate can't exist for the set of distributions. In this paper we obtain the optimal convergence rates for a class of distributions λ,ω in multicategory classification and nonstandard binary classification.关键词: rate of convergence,error probability,modulus of continuity...
It is a method proposed more than thirty years ago, but somehow there has not been any theoretic result on its convergence rate in the literature. In this paper, we fill the gap by establishing minimax optimal convergence rates for Dawid-Skene estimator. We obtain a lower bound which holds ...
Particularly, the paper establishes the optimal rate of convergence in two steps for the minimax sup-norm risk of convex functions with the H"older order between one and two. In the first step, by applying information theoretical results on probability measure distance, we establish the minimax ...
Minimax estimationOperator normOptimal rate of convergenceCovariance structure plays an important role in high-dimensional statistical inference. In a range of applications including imaging analysis and fMRI studies, random variables are observed on a lattice graph. In such a setting, it is important ...
as well as a new analysis. We also consider the stochastic case, and prove that an appropriate modification of the upper confidence bound policy UCB1 (Auer et al., 2002) achieves the distribution-free optimal rate while still having a distribution-dependent rate logarithmic in the number of pl...
To obtain the minimax convergence rate for the first case, we will use a two-point argument going all the way back to Ibragimov and Has’minskii [8] and Has’minskii [7]. First, we need to define an appropriate “test” function. We will use the optimal bandwidth hn=n−12α+q ...